A new geomechanical model is presented in which the rock mass is treated as an elastic, composite material. Here the joints are treated as weak laminae in a strong matrix of rock. Basic equations for two crossings sets of joints are presented and applied to the rock mass of the Nasliden mine. Application of the theory of transversely isotropic material with stiffness data taken from shear box experiments gives too low values of the equivalent elastic moduli of the rock mass. The geomechanical model can be used to assess the rock mass properties for input into anisotropic, elastic finite-element analysis of structures in rocks.