The mathematical formulation of the Porous Media System, (PMS) describing two-phase, immiscible, compressible, fluid flow in linear, homogeneous porous media is reviewed and expanded. It is shown that families of common vertex, coaxial parabolas and families of parallel lines are the only families of curves on which solutions of the PMS may be constant. A coordinate transformation is used to change the partial differential equations of the PMS to a system of ordinary differential equations, referred to as a Similarity Porous Media System (SPMS), in which the independent variable denotes movement from curve to curve in a selected family of curves. Properties of solutions of the first boundary value problem are developed for the SPMS.