The propagation of a crack during cyclic loading with large plasticity was simulated using a finite element method. The numerical procedure included the determination of crack closing and opening by examining the contact condition of the crack surfaces in the plasticity iteration. The method was applied to the growth of cracks in Alloy 718 single edge notch specimens at 538°C subject to Rϵ = -1 strain cycling under both nominally elastic and elastic-plastic conditions. Experimentally measured remote displacements were used to establish the boundary conditions for the finite element analysis. The measured load and crack mouth opening displacement were used to verify the results. The results show, among other things, that the crack closure and opening stresses become more compressive as the loading becomes more plastic, and that, under a given control condition, the closure and opening stresses become less compressive as the crack propagates.