In this paper we will show how the recently introduced deformation field method [Peters et al. (1999) and van Heel et al. (1999)] can be generalized to complex flow simulations of nontime-strain separable integral constitutive models. To illustrate this generalization we start with the time-strain separable Doi-Edwards model and we show how the approach can be generalized to nontime-strain separable models. As an example of such a model we consider the reptation model which was recently introduced by Mead et al. [Mead et al. (1998)]. In this reptation model also tube-stretch and convective constraint release are taken into account. We use both models to simulate startup of two-dimensional flow past a cylinder positioned between two parallel plates. (C) 2000 The Society of Rheology. [S0148-6055(00)00804-X].