This paper deals with a procedure to calculate the elastic stress intensity factors for arbitrary-shaped cracks in plane stress and plane strain problems. An assumed displacement hybrid finite element model is employed wherein the unknowns in the final algebraic system of equations are the nodal displacements and the elastic stress intensity factors. Special elements, which contain proper singular displacement and stress fields, are used in a fixed region near the crack tip; and the interelement displacement compatibility is satisfied through the use of a Lagrangean multiplier technique. Numerical examples presented include: central as well as edge cracks in tension plates and a quarter-circular crack in a tension plate. Excellent correlations were obtained with available solutions in all the cases. A discussion on the convergence of the present solution is also included.