With advances in physiological sensors, we are able to understand people's physiological status and recognize stress to provide beneficial services. Despite the great potential in physiological stress recognition, there are some critical issues that need to be addressed such as the sensitivity and variability of physiology to many factors other than stress (e.g., physical activity). To resolve these issues, in this paper, we focus on the understanding of physiological responses to both stressor and physical activity and perform stress recognition, particularly in situations having multiple stimuli: physical activity and stressors. We construct stress models that correspond to individual situations, and we validate our stress modeling in the presence of physical activity. Analysis of our experiments provides an understanding on how physiological responses change with different stressors and how physical activity confounds stress recognition with physiological responses. In both objective and subjective settings, the accuracy of stress recognition drops by more than 14% when physical activity is performed. However, by modularizing stress models with respect to physical activity, we can recognize stress with accuracies of 82% (objective stress) and 87% (subjective stress), achieving more than a 5-10% improvement from approaches that do not take physical activity into account.