People react differently to stress. According to the Cognitive Motivational Relational Theory by Lazarus and Folkman, the appraisal of stress and the emotions related to it determine whether people cope with stress by focussing on altering the situation (problem focussed) or on changing the emotional consequences of the events (emotion focussed). These different coping strategies have different effects on the long term. The coping process can be described in a formal dynamic model. Simulations using this model show that problem focussed coping leads to better coping skills and higher decrease of long-term stress than emotion focussed coping. These results also follow from a mathematical analysis of the model. The presented model can form the basis of an intelligent support system that uses a simulation of cognitive processes in humans in stressful conditions.