I don't know hydrodynamics, but I wonder how one would compute resonance modes of a cubic box of water which we shake. I believe the waves would directly depend on the height of water and the width and length of the box. Is it a bit like a waveguide for electodynamics?
Yes it is a bit like waveguide for electrodynamics. You've got absolutely the same equation. The difference is in boundary conditions -- instead of Dirichlet you've got to use Neumann boundary conditions.
While of course it works only if you are able no neglect all the non-linear effects -- your waves are low enough.