In many areas of chemical engineering applications we have to deal with thermosetting polymer structures. One of the major processing techniques for producing such structures is the curing process. This process may be accompanied by undesirable thermal spiking phenomena during which the released energy may be trapped inside of the structure. In order to predict the onset of this phenomenon models that couple reaction kinetics and heat transfer are required. In this paper we propose an efficient algorithm for the solution of such coupled problems. The algorithm is based on the alternating-triangular methodology which is more efficient compared to ADI methodologies conventionally applied to similar problems. The algorithm is described in detail. The results for simulations of reaction kinetics are compared with those obtained in the literature from experimental measurements. A series of numerical experiments for the fully coupled system are also presented. (C) 2003 Elsevier Science Ltd. All rights reserved.