Analytical solutions are developed for the response of saturated porous media under twodimensional plane strain condition. Depending on the nature of loading vis-à-vis the characteristics of the media, different formulations (fully dynamic, partially dynamic, quasi-static) are possible. The solutions for these formulations are developed in terms of non-dimensional parameters. The regions of validity for the three formulations are identified in a parametric space. An assessment of the needed formulation for few geomechanics problems is presented.