This research utilizes machine learning models to detect equity bubbles and predict financial crashes in the S&P 500 index. The imbalanced data problem is addressed, where non-bubbles significantly outnumber bubbles in the training data. Model features are selected based on economic theories and market fundamentals. The Random Forests model, with a Cross-Validation-tuned decision threshold, demonstrates the highest performance with a 93.0% balance accuracy rate. The model effectively balances sensitivity (100%) and specificity (86%). However, the Recurrent Neural Networks with Bidirectional Long-term Short Memory and focal loss function yield unsatisfactory results, likely due to limited data size. Key predictive features include market fundamental indicators, long-term market returns, and the psychology factor. Short-term market returns and macroeconomic indicators are less influential in crash prediction. The model focuses on long-term (over 3 months) and extreme market downturns. In conclusion, this research provides a machine learning approach to predict financial crashes and detect equity bubbles in the S&P 500 index. The Random Forests model effectively addresses imbalanced data, while highlighting the significance of market fundamentals. Limitations include the performance of Recurrent Neural Networks and the scope of long-term extreme market downturn predictions. These findings contribute to risk assessment and market forecasting in finance.