A matrix formalism developed by Thomson and Haskell to study the transmission of plane elastic waves through a system of parallel, homogeneous, isotropic layers is extended to the case of parallel poroelastic layers. In a poroelastic medium, there are two dilatation waves and one rotational wave contrasted with one rotational wave and only a single dilatation wave for ordinary elastic media. Formal matrices are obtained which allow the systematic computation of transmission of these waves through layered poroelastic media.