Stress is a complicated physiological and psychological phenomenon that has a huge impact on the health and performance of people. Conventional methods of measuring stress are dependent upon self-reports, making it difficult to determine if they are truthful and cannot be noted in real-time. In this study, the use of machine learning techniques to identify stress objectively based on physiological signals taken from ECG and EEG was examined. While other studies have only examined one signal type (either ECG or EEG), this study compared the two modalities side-by-side under the same experimental conditions, using equal amounts of data from publicly available datasets. Multiple machine learning models (Logistic Regression, Support Vector Machine, Random Forest, XGBoost, LSTM) were compared and contrasted using available datasets. Physiological signal features (heart rate variability, electrodermal activity) were taken into account and analysed to understand both autonomic and neural activation due to stress. The results demonstrated that the Random Forest model yielded the highest level of performance (F1-score=.86, AUC=.90), indicating that Random Forest is better suited to handling complex physiological signals than any other machine learning model. An analysis of the physiological signals indicated that stress causes a decrease in heart rate variability, an increase in skin conductance, and an increase in cardiovascular activity (during the physical response) due to increased sympathetic nervous system stimulation. In summary, this research points to machine learning-based techniques yielding dependable, non-invasive means for detecting stress. This research indicates that there is an opportunity to use physiologic signal analysis in combination with AI to provide future possibilities for monitoring mental health and wearable technology.