Stress remains a significant social problem for individuals in modern societies. This paper presents a machine learning approach for the automatic detection of stress of people in a social situation by combining two sensor systems that capture physiological and social responses. We compare the performance using different classifiers including support vector machine, AdaBoost, and k-nearest neighbour. Our experimental results show that by combining the measurements from both sensor systems, we could accurately discriminate between stressful and neutral situations during a controlled Trier social stress test (TSST). Moreover, this paper assesses the discriminative ability of each sensor modality individually and considers their suitability for real time stress detection. Finally, we present an study of the most discriminative features for stress detection.