Finite element methods are applied to the analysis of squeeze films between porous surfaces. Planar elements in the fluid film region are joined with solid elements in the porous region to ensure continuity of pressures and flows. The formulation is valid for problems with irregular geometry and nonhomogeneous anisotropic permeability. A simple example with uniform properties demonstrates convergence to a previous analytical solution. More complex examples illustrate the power and versatility of the method.