Phased array antennas are key components in advanced communication systems. The synthesis of their radiation patterns plays a vital role in designing and shaping desired radio beams for various applications. Traditionally, numerous analytical and numerical methods have been used to achieve desired radiation patterns. However, these methods often require complex and time-consuming computations or cannot be implemented for all desired patterns. As a result, artificial intelligence algorithms, particularly machine learning models, have emerged as a novel approach for radiation pattern synthesis. In this study, two machine learning algorithms—Support Vector Machine (SVM) and Gaussian Process Regression (GPR)—were employed to synthesize the radiation pattern of a linear phased array antenna with uniform spacing. A notable advantage of this method is its low demand for training data (only about 27 training datasets) and fast training speed, with both models training in less than a second for linear arrays with 15 radiating elements. Additionally, sensitivity analysis shows that the Gaussian Process Regression algorithm achieves higher accuracy than the Support Vector Machine, with a mean squared error of less than 0.001 for conventional patterns and below 0.01 for patterns with discontinuities. Thus, GPR can be considered a suitable option for the advanced design of antenna arrays in communication and radar applications.