Hydraulic comminution is especially suitable if the elastic properties of the components differ significantly. Here, the basic equations of the elasticity theory were drafted for two model shapes. In cylindrical as well as in Cartesian coordinates, the solution to the equation system is obtained through the solution of the bipotential equation via the introduction of a stress function. However, certain boundary conditions have to be fulfilled. In the case of all-round constant compression, this can be achieved through an approach in integral form for both model shapes.