Pricing American options accurately is of great theoretical and practical importance. We propose using machine learning methods, including support vector regression and classification and regression trees. These more advanced techniques extend the traditional Longstaff-Schwartz approach, replacing the OLS regression step in the Monte Carlo simulation. We apply our approach to both simulated data and market data from the S&P 500 Index option market in 2019. Our results suggest that support vector regression can be an alternative to the existing OLS-based pricing method, requiring fewer simulations and reducing the vulnerability to misspecification of basis functions.