In a continuum approach to concrete fracture a gradient-dependent plasticity theory is used to preserve the well-posedness of the problem in the softening regime and to obtain finitely sized fracture process zones. The theory employs a Rankine failure surface dependent on the Laplacian of a fracture strain measure. The finite element algorithm assumes a discretization of fracture strains in order to solve the differential consistency equation. A class of C1 and C0-continuous finite elements have been developed.