This is where you need to work on mesh refinement. You want to make the mesh finer until the results are constant (taking into account that sometimes finer mesh will make local maxima (like corners) artificially large).
What Chris Michalski said but also pay close attention to mesh quality. With poorly shaped mesh (i.e. lots of slivers) you will get very poor results. Also, and I can't stress this enough, do some hand calculations to see if what you are seeing is 'reasonable'.
Search the forums and read up about deflection convergence. That is key rather than focusing on stress exclusively.