The prediction of the macroscopic behaviour of Flemish bond brickwork (FBB) is dealt with. From the finite element analysis of a representative volume element (RVE) of masonry, assumed to be a heterogeneous medium with periodic properties along two perpendicular directions, information on the macroscopic mechanical properties of masonry is obtained. The RVE is subjected to particular boundary conditions, which match the periodicity of the medium, to predict its response under elementary macroscopic stresses. The model takes into account the nonlinear behaviour of mortar and bricks by means of a combined plasticity and damage model. The macroscopic strength and post-peak behaviour of FBB under elementary in- and out-of-plane stresses are predicted. The biaxial macroscopic strength domain of masonry subjected to in-plane stress is also predicted for different orientations of the maximum principal stress to the bed joints.