Chronic stress poses serious harm to both physical and mental health. It is a risk factor for hypertension and coronary artery disease, as well as other health problems including gastroesophageal reflux disease (GERD) and mental illnesses such as anxiety. It is currently challenging for individuals to track their own stress when current methods only allow for discrete stress measurements. As wearable medical sensors (WMSs) become more commonplace, though, physiological signals such as electrocardiogram (ECG), galvanic skin response (GSR), respiration rate, blood pressure, and blood oximeter become much more accessible. By combining these sensors with a machine learning model, we will be able to continuously monitor human stress levels to detect high levels of stress in a user-transparent manner. However, diagnosis solely based on WMS data remains challenging due to the resource-intensive characteristic of feature extraction. To address this problem, we propose a framework called StressDeep that combines efficient neural networks with off-the-shelf WMSs for stress detection. We demonstrate the effectiveness of StressDeep on data collected through the SoDA experiment, which uses traditional machine learning models to both detect and alleviate stress. As the dataset is limited to only 32 participants, we developed a synthetic dataset to impose a prior on the DNN weights. The addition of synthetic data boosted the accuracy of the various DNNs and our highest test accuracy obtained was 75.2%. We also compare StressDeep against the baseline methods used in SoDA, such as support vector machines, k-nearest neighbor, and random forest, to determine differences in performance.