Mudstones are nearly ubiquitous in sedimentary basins and yet remain perhaps the most poorly understood lithology from a geophysical perspective. In particular, density and neutron logging measurements of mudstone porosity conflate the mechanically dis tinct porosities of both immoveable (bound) water and moveable (pore space) water. Immoveable water is mechanically part of the crystalline structure of the mudstone and contributes to both the bulk modulus and shear modulus of the rock. Moveable water in the pore spaces contributes to the bulk modulus of the saturated rock, but not to the shear modulus. Models of mudstones should be consistent with all known geophysically measurable properties of mudstones. Some obvious geophysical properties to start with are total porosity (or equivalently, density), P-wave velocity, and S-wave velocity. Earlier model ing of mudstones by others utilized the Hashin-Shtrikman lower and upper bounds. Those workers were able to produce P-wave and S-wave velocities from their model that replicated their shale laboratory measurements. Nevertheless, that model leaves a bit to be desired. That mathematical model assumes spherically concentric distribution of elastic materials for constituent particles, which is not consistent with tabular clay min erals which can be described as platelets. I propose an alternative mathematical model, described previously by another worker, which assumes flat plates. This is more consistent with the repeated unit-cell geometries that characterize individual clay platelets. Total porosities from the litera ture are used as bounding constraints on the model, and the model separates the move able and immoveable porosities based upon observations of clay compaction behavior. P-wave and S-wave velocities from this new model compare favorably with field and laboratory measurements. Better modeling of mudstones should ultimately lead to fewer surprises in practical pressure prediction as the mudstone effective-stress relationship becomes better understood.