The partial differential governing equation governing fluid infiltration into an unsaturated transversely isotropic porous medium was developed by considering mass conservation, Darcy’s law, and the elastic deformability of the porous skeleton. Analytical solutions for two-dimensional coupled infiltration in an unsaturated porous medium of finite extent were obtained using a Fourier transform technique. The analytical formulation was used to examine the two-dimensional infiltration and evaporation problem for a transversely isotropic unsaturated porous medium. This study provides a comparison between the analytical solution and computational estimates for a two-dimensional coupled infiltration problem in a transversely isotropic deformable porous region where there is recharge at the surface. The results indicate that the pressure head changes occur most rapidly when the unsaturated porous medium is hydraulically isotropic.