A method for determining fractured rock mass properties is presented here on the basis of homogenisation approach. The rock mass is considered to be a heterogeneous medium composed of intact rock and of fractures. Its constitutive model is studied numerically using Finite Element Method and assimilating the fractures to joint elements (Coste1). The method has been applied to a granite formation in France. Geological data on different families of fractures have been used for the statistical representation of the fractures. A mesh-generating tool for the medium with high density of fractures has been developed. The mechanical behaviour of the rock mass (elasticity, ultimate strength and hardening law) has been determined assuming linear elasticity and Mohr-Coulomb strength criterion both for the intact rock and the fractures. Evolution of the mechanical strength in different directions has been determined as a function of the mean stress, thanks to various numerical simulations. The mechanical strength appears to be anisotropic due to the preferential orientation of the fractures. The numerical results allowed us to determine an oriented strength criterion for the homogenized rock mass. A 2D constitutive law for the homogenized medium has been deduced from numerical data. A 3D extension of this model is also presented.