You can install one Ubuntu system (typically an Ubuntu Server system, but it does not have to be), and then use it as a server to PXE boot and install the others. The BIOSes on the clients (where you want to install Ubuntu) must support PXE (i.e., network boot) for this to work. But most BIOSes do, these days.

You should be able to do it with a non-Ubuntu system as the host, too, if you already have that set up and you know how to configure the necessary servers on your non-Ubuntu system.

The PXEInstallServer Ubuntu help wiki article explains how to set up an Ubuntu system as your PXE server, and how to install Ubuntu on other systems from it. It would be hard to summarize the main points--the details are very important. So here's the whole thing (with minor formatting and punctuation changes):

Introduction

This will guide you through running an Ubuntu server as PXE install
server. You'll need to run a DHCP server on your network, not
necessarily this server but you do need one.

Installing needed packages

You'll need to install the following packages: inetutils-inetd
(previously netkit-inetd), tftpd-hpa (see
InstallingSoftware).

For Ubuntu 10.04, there is a bug with inetutils-inetd. It only listens on IPv6, and not on IPv4. As a quick workaround, you can use
openbsd-inetd instead.

If this is also going to be your DHCP server, install dhcp server
contained in the follwing package: dhcp3-server (see
InstallingSoftware).

Configure tftpd-hpa

You'll need to tell tftpd-hpa to start its daemon (which it doesn't by
default). To do this, edit the /etc/default/tftpd-hpa file, and make
sure that it looks something like this:
#Defaults for tftpd-hpa

RUN_DAEMON="yes"

OPTIONS="-l -s /var/lib/tftpboot"
Then, run the startup script to actually start the daemon:
/etc/init.d/tftpd-hpa restart
Configure dhcpd

If your pxe server is also your dhcp server, you'll need something
like this in /etc/dhcp3/dhcpd.conf:
subnet 192.168.0.0 netmask 255.255.255.0 {

        range 192.168.0.100 192.168.0.200;

        filename "pxelinux.0";

}
If you have an existing dhcp server, you should point it to your pxe
server by doing something like the following:
subnet 192.168.0.0 netmask 255.255.255.0 {

    <other config here>

    filename "pxelinux.0";

    next-server <pxe host>;

}
Be sure to restart your dhcp server so that the changes take effect:
sudo /etc/init.d/dhcp3-server restart
Configure tftpd-hpa

tftpd-hpa is called from inetd. The options passed to tftpd-hpa
when it starts are thus found in /etc/inetd.conf

The defaults are fine for us, your /etc/inetd.conf should have an
entry like this:
tftp    dgram   udp    wait    root    /usr/sbin/in.tftpd /usr/sbin/in.tftpd -s /var/lib/tftpboot
(Although you may need to edit this file and replace udp with
udp4, as tftpd-hpa seems to expect an IPv6 address now.)

Now we'll copy the needed files from the Ubuntu CD:
sudo cp -r /media/cdrom/install/netboot/* /var/lib/tftpboot/
If your dhcp server issues correct network info and your pxe clients
will have network access, then at this point you will be able to do an
Ubuntu install using internet repositories.

I want to go a little further however and install everything from the
install server as well as customise some of the packages to install.

Install apache

Currently nfs installs aren't well supported (please correct me if I'm
wrong) so we'll install over http. For that we need a webserver on our
install server too: install the following package: apache (see
InstallingSoftware).

Copying Ubuntu files

Create an ubuntu directory under your freshly installed apache's
document root and copy all of the contents of the Ubuntu Alternate CD
to that directory:
mkdir /var/www/ubuntu

cp -r /media/cdrom/* /var/www/ubuntu/
Customising the install

There is a package called system-config-kickstart which is a GUI
frontend to creating kickstart files. The kickstart file tells the
installer where to get its packages from, what to install and a number
of other useful settings. See KickstartCompatibility for more
info.

This package does not have to be installed on your install server, it
can be on a convenient Ubuntu desktop somewhere.

Create a custom ks.cfg with system-config-kickstart, be sure to
specify HTTP under "Installation Method". Provide the IP of you
install server and make the HTTP Directory /ubuntu/. Save the file
and copy it to your install server under /var/www/html/.

A very minimalist `ks.cfg file which only uses the installation files
on the install server and asks for all other questions might look like
this:
install

url --url http://192.168.0.1/ubuntu/
Use your ks.cfg

In order for your network Ubuntu install to use your kickstart file,
you have to tell it where to find it. Edit
/var/lib/tftpboot/pxelinux.cfg/default and add
ks=http://<installserver>/ks.cfg to the append line. It should then
look something like this (note that the append line is one line):
label linux

        kernel ubuntu-installer/i386/linux

        append ks=http://192.168.0.1/ks.cfg vga=normal initrd=ubuntu-installer/i386/initrd.gz ramdisk_size=16432
root=/dev/rd/0 rw --

In Jaunty [and presumably later releases, including any release
you're likely using]¹ the default file has been broken
up into includes. The append line can be found in
/ubuntu-installer/i386/boot-screens/text.cfg:
label install

        menu label ^Install (from my http server)

        menu default

        kernel ubuntu-installer/i386/linux

        append ks=http://192.168.0.1/ks.cfg vga=normal initrd=ubuntu-installer/i386/initrd.gz -- quiet
Boot and install

You should now be able to boot another pc on the lan over the network
and have it install Ubuntu automagically. :) You can vary the tftp and
http install points to have multiple versions of Ubuntu available to
install on your network.

Using the CD (or .iso) directly

You can also achieve the above without actually copying any files
anywhere. You can mount the CD (or the .iso) and then do additional
mounts with the --bind option. The advantage is that you can upgrade
the CD (or the .iso) without needing to update the install server
files.

For example, after mounting the CD (or the .iso) to /media/cdrom/,
you can mount the ubuntu files to the web directory:
mount --bind /media/cdrom/ /var/www/ubuntu/
Similarly, you can do the same with the tftproot:
mount --bind /media/cdrom/install/netboot/ /var/lib/tftpboot/
If you were to create a pxelinux.cfg directory with an appropriate
default file, you can mount that over the top of the mounted CD, so
that the tftp server gives out your pxelinux.cfg/default file. For
example, a pxelinux.cfg directory in ~/pxelinux.cfg could be
mounted like this:
mount --bind ~/pxelinux.cfg /var/lib/tftpboot/pxelinux.cfg
(Note that in the above example, the actual mount point of the
directory would end up as
/var/lib/tftpboot/ubuntu-installer/i386/pxelinux.cfg because the
pxelinux.cfg is a symlink on the CD (or .iso)).

— PXEInstallServer, with slight formatting, punctuation, and capitalization changes, mainly to accomodate the Ask Ubuntu Format.

That article is from the Ubuntu documentation wiki. It was written by "Contributors to the Ubuntu documentation wiki" and is licensed under CC-BY-SA 3.0, which allows inclusion here, with proper attribution.

¹[Bracketed italicized text] is not from the original; it is my commentary.

Note the difference between this method and the method Mitch suggested. That method involves booting from a CD/DVD or USB flash drive, which then installs the system over a network. By default this network is the Internet; for that method to be reasonable for installing to hundreds of machines on a network, you would probably want to create and host an Ubuntu repository on your network, and point your installations to that.

The effort and infrastructure necessary to do that is comparable to what would be necessary to PXE boot the machines as described above. So while that way might meet your needs, I'd encourage you to consider PXE booting if you really need to install without "physical media."