Predicting Bispectral Index (BIS) and Mean Arterial Pressure (MAP) during anesthesia is critical for patient safety and effective anesthesia management. Traditional pharmacodynamic response surface models have limitations in accuracy and adaptability. This paper presents a novel approach for predicting BIS and MAP using machine learning techniques. Rather than using standard pharmacodynamic response surface models, a machine learning-based approach is proposed to model the pharmacodynamic. The proposed method considers the state of the standard propofol and remifentanil pharmacokinetic model and the patient information as features to predict the BIS and MAP values. Training and testing are done on a selected subset of the VitalDB dataset (Lee and Jung, 2018) containing 191 different patients. Results demonstrate that the machine learning-based approach outperforms standard pharmacodynamic models in terms of accuracy. Specifically, the Support Vector Regression (SVR) model achieves a Mean Absolute Prediction Error (MDAPE) 32% smaller than the Eleveld model for BIS prediction. For MAP prediction, the SVR model also demonstrates superior performance with a reduction of 66% of MDAPE. The proposed method provides similar performance as the deep-learning method (Lee et al., 2018) while keeping a simple structure that may be used in other applications.