Applying a direct formulation for the enrichment of the displacement field an extended finite element (XFEM) scheme for modeling of cohesive crack growth is developed. Only elements cut by the crack is enriched and the scheme fits within the framework of standard FEM code. The scheme is implemented for the 3-node constant strain triangle (CST) and the 6-node linear strain triangle (LST). Modeling of standard concrete test cases such as fracture in the notched three point beam bending test (TPBT) and in the four point shear beam test (FPSB) illustrates the performance. The XFEM results show good agreement with results obtained by applying standard interface elements in FEM and with experimental results. In conjunction with criteria for crack growth local versus nonlocal computation of the crack growth direction is discussed.