The possibility of enhancing a B-spline basis with discontinuities by means of knot insertion makes isogeometric finite elements a suitable candidate for modeling discrete cracks. In this contribution we use isogeometric finite elements to discretize the cohesive zone formulation for failure in materials. In the case of a pre-defined interface, non-uniform rational B-splines are used to obtain an efficient discretization. In the case that propagating cracks are considered, T-splines are found to be more suitable, due to their ability to generate localized discontinuities. Various numerical simulations demonstrate the suitability of the isogeometric approach to cohesive zone modeling. Copyright © 2010 John Wiley & Sons, Ltd.