Measuring resilience to stress (or stress resistance) validly and reliably is an important theoretical and practical problem. Process-oriented stress theories assume that primary and secondary appraisals play an important role in determining the level of resilience. In the present study, a model of resilience based on the analysis of the interplay between primary and secondary appraisal processes is developed. Resilience is high if benign primary appraisals of taxing situations are accompanied by secondary appraisals of coping resources as being sufficient for controlling stressors. In an implementation of the model, the quality of primary appraisals is assessed through the assessment of anxiety, anger and depression, which characterize the most typical cognitive-emotional reactions to demanding situations. The assessment of secondary appraisals is restricted to the analysis of psychophysiological (functional) resources, which are involved in all forms of coping activities. The implementation of the model gives rise to a measure of resilience, which is shown to successfully predict the outcome of the stress process in a sample of Russian police officers.