Based on the continuous plane-strain deformation of an isotropic, frictional, cohesive, compressible solid, a rolling theory for granular solids has been developed. The pressure exerted by the press is predicted as a function of the flow properties of the solid, roll size, roll gap, roll surface condition, and feed pressure. Calculated results of the theory are presented in terms of roll-separating force, roll torque, and the ratio of maximum to minimum pressure existing in the press. Examples of the effect of material properties on these results are given.