Support vector machines (SVMs) are a good candidate for the solution of antenna array processing problems such as beamforming, detection of the angle of arrival, or sidelobe suppression, due to the fact that these algorithms exhibit superior performance in generalization ability and reduction of computational burden. Here, we introduce three new approaches for antenna array beamforming based on SVMs. The first one relies on the use of a linear support vector regressor to construct a linear beamformer. This algorithm outperforms the minimum variance distortionless method (MVDM) when the sample set used for training is small. It is also an advantageous approach when there is non-Gaussian noise present in the data. The second algorithm uses a nonlinear multiregressor to find the parameters of a linear beamformer. A multiregressor is trained off line to find the optimal parameters using a set of array snapshots. During the beamforming operation, the regressor works in the test mode, thus finding a set of parameters by interpolating among the solutions provided in the training phase. The motivation of this second algorithm is that the number of floating point operations needed is smaller than the number of operations needed by the MVDM since there is no need for matrix inversions. Only a vector-matrix product is needed to find the solution. Also, knowledge of the direction of arrival of the desired signal is not required during the beamforming operation, which leads to simpler and more flexible beamforming realizations. The third one is an implementation of a nonlinear beamformer using a non-linear SVM regressor. The operation of such a regressor is a generalization of the linear SVM one, and it yields better performance in terms of bit error rate (BER) than its linear counterparts. Simulations and comparisons with conventional beamforming strategies are provided, demonstrating the advantages of the SVM approach over the least-squares-based approach.