The response of saturated porous medium is of significant interest in many fields ranging from geomechanics to biomechanics. Biot was the first to formulate the basic equations governing the process of coupled flow and deformation in porous media. Depending on the nature of loading vis‐à‐vis the characteristics of the media, different formulations (fully dynamic, partly dynamic, quasi‐static) are possible. In this study, analytical solutions are developed for the response of saturated and nearly saturated porous media under plane strain condition. The solutions for different formulations are developed in terms of non‐dimensional parameters. The response is studied for various conditions and the regions of validity for various formulations are identified in a parametric space. An assessment of the needed formulation for few important problems is also presented. Copyright © 2008 John Wiley & Sons, Ltd.