What version of Premiere Elements are you using and on what computer operating system is it running?
For now I will generalize and then customize an answer for you based on the details that you supply.
You can export a file with a .mp4 file extension in either of two routes....using Premiere Elements 12 on Windows 7, 8, or 8.1 64bit as the model...
a. Publish+Share/Computer/AVCHD and one of the MP4 presets.
b. Publish+Share/Mobile Phone and Players/Apple iPod, iPad, iPhone and one of its presets
Remember that .mp4 is just a file extension (a wrapper/container format) which wraps the video and audio compressions of a file. So in your Premiere Elements exports you may have to take into consideration what you want in the way of compression as well as file extension, depending on the file's use requirements.
Looking forward to your follow up.
I am using Premiere Pro CC version 7.1