Our objective is to model static multi-cracking processes in concrete. The explicit dynamic relaxation (DR) method, which gives the solutions of non-linear static problems on the basis of the steady-state conditions of a critically damped explicit transient solution, is chosen to deal with the high geometric and material non-linearities stemming from such a complex fracture problem. One of the common difficulties of the DR method is its slow convergence rate when non-monotonic spectral response is involved. A modified concept that is distinct from the standard DR method is introduced to tackle this problem. The methodology is validated against the stable three point bending test on notched concrete beams of different sizes. The simulations accurately predict the experimental load-displacement curves. The size effect is caught naturally as a result of the calculation. Micro-cracking and non-uniform crack propagation across the fracture surface also come out directly from the 3D simulations.