Your terminology may lead people astray. In my field the eigenvalue is the frequency of a resonant mode. If you mean, how do you calculate the buckling strength of a flat plate, I suspect Mr Roarke's book or Timoshenko is the place to start.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376
The eigenvalue solver can be used for both natural frequency and buckling problems.
For plates that are orthotropic in bending, you can find some basic solutions in MIL-HDBK-17. There are quite a few more solutions in "Mechanics of Composite Structures" by Kollar and Springer.