It should run just fine on Yosemite. In fact, that's the version of OSX it was designed for!
Although there is an update for version 13 that will take it to version 13.1. (In fact, you'll be prompted to download it the first time you launch the program.) It may improve your performance -- but if the program is not running at all, it may not fix it either. You've got something more serious going on.
How are you trying to launch the program and what's happening when you try it? Or are you saying that it won't even install? If the latter, where did you get the program? Did you download it from the Adobe site?
Thank you for the response so quickly. But i also solved my own problem just as quick. I was double clicking on the Icon in my Applications meny of the Finder and it was popping up with a message that read "Premiere Elements 13 is on OS X program and cannot be run". I did that a couple times and thats when i posted the question. I then right clicked the Premiere icon and click Open, and it opened no problem. Not sure why the double click, and right click "open", act differently but my Problem is solved.
Your response is very much so appreciated non-the-less.
Glad you got it running, Bryan.
Don't forget -- when you drag the program to your Dock to create a shortcut, make sure you're dragging down the execution file for the program itself and not the Premiere Elements folder or it won't work.