AbstractThe phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all structures. They may exist as basic defects in the constituent materials or they may be induced in construction or during service life.Using the finite element method, a lot of papers deal with the calculation of stress intensity factors for two‐ and three‐dimensional geometries containing cracks of different shapes under various loadings to elastic bodies. In order to increase the accuracy of the results, special elements have been used. They are described together with methods for calculating the stress intensity factors from the computed results.At the vicinity of a crack tip, the strains are not always small, but they may also be large. In this case, the J‐integral can also be applied to characterize the cracks in elastic or elastic–plastic bodies.This paper describes the computation of the two‐dimensional J‐integral for large strains to elastic and elastic–plastic bodies and represents some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.