A new boundary element formulation in two-dimensional rate-independent plasticity is given. This new formulation uses a so-called traction-free fundamental solution so that the resulting boundary integral equation converges in the normal sense, and more important, a formal differentiation of the boundary integral equation leads to a valid integral representation for the in-plane stress component on the boundary. No finite difference approximation is needed to construct the stress recovery routine. The new boundary element method is then used to solve the problem of quasi-static ductile crack growth. Numerical simulations based on a set of experimental data have been carried out to evaluate a new path-independent integral, T* M . The T* M ,-integral is a modified version of Atluri's T*-integral. This modified version has an advantage of having a less singular domain integral near the crack flank so that it is numericaly preferable to T*.