I can run ePSXe in Ubuntu 14.04. So I think it should work in previous Ubuntu versions as well. It took me some days of trial and error until I found a decent solution. I have a 64 bit machine and can't assure this is going to work with a 32 bit operating system.
sudo dpkg -i libstdc++2.10-glibc2.2_2.95.4-27_i386.deb
sudo dpkg -i libglib1.2ldbl_1.2.10-19build1_i386.deb
sudo dpkg -i libgtk1.2-common_1.2.10-18.1build2_all.deb
sudo apt-get install libsdl-ttf2.0-0:i386
sudo apt-get install gtk2-engines:i386
I don't know if the next packages are necessary but there will be no harm on installing them:
sudo apt-get install libgtk2.0-0:i386
sudo apt-get install gtk2-engines-murrine:i386
sudo apt-get install libcanberra-gtk-module:i386
sudo apt-get install unity-gtk2-module:i386
If you are going to use spuEternal sound plugin (it's my favorite) you should download
libsdl1.2debian_1.2.15-5ubuntu1_i386.deb and extract its contents to copy the shared libraries. You need
libSDL-1.2.so.0 (which is a symlink). Copy those two a any place you want (I like to create a subdirectory inside of epsxe directory).
libgtk1.2_1.2.10-18.1build2_i386.deb contents and all lib directory contents to the lib directory (inside epsxe directory) you created on the previous step.
Now go the lib directory (the one you have just created) and do this:
ln -s libSDL-1.2.so.0.11.4 libSDL.so
In order to configurate spuEternal plugin the previous step is necessary.
Now create a bash to run ePSXe:
I hope this can be helpful :)