As you indicate that it might have something to do with boundary conditions, is your model undersconstrained? That is, are the rigid body modes present?
One simple way of finding out is to run an eigenfrequency analysis. If there are any modes with f=0 Hz the graphics might indicate what your problem is. Also, just a simple tip. Have you checked for coincident nodes?
For more ideas I/"we" would probably need more information what kind of sigularity problem you have?
