The lattice equivalent continuum model (LECM) has proved to be very effective in analysing reinforced concrete structures in two-dimensional cases. That model is extended here to three dimensions and is fitted to a finite element formulation for analysing three-dimensional reinforced concrete structures. In any of the three principal directions, the stress-strain behaviour of concrete will be affected by the stress state in the other two directions. Consequently, stress-strain curves for concrete will shift from a uniaxial pattern. This phenomenon is considered in this work by selecting concrete peak stresses in three alternative approaches. The effectiveness of those approaches is also evaluated. The results of the calculations show good reproduction of the test data, which indicates the validity of this proposed 3D modelling of reinforced concrete.