This paper describes the characterization of reflectarray unit cells using Support Vector Machines (SVMs) to obtain fast and accurately the full matrix of reflection coefficients, which is used for an analysis of dual-polarized reflectarrays, demonstrating the performance of the model. First, a surrogate model of the reflectarray unit cell is obtained using SVMs. To this end, a set of random samples of the reflection coefficient matrix with a full-wave Method of Moments based on Local Periodicity (MoM-LP) is used to train the SVMs. To efficiently obtain the surrogate model, a novel strategy to accelerate the training process is presented, remarkably reducing computing time. Next, the model is tested against a different set of samples, obtaining an excellent agreement between the SVM model and MoM-LP simulations for all reflection coefficients, including the crosscoefficients. The surrogate model is then used for an efficient analysis of three reflectarrays with pencil beam for point-topoint communications, isoflux pattern for global Earth coverage, and a shaped-beam for Local Multipoint Distribution Service application, showing excellent agreement in both copolar and crosspolar patterns between the SVM and MoM-LP simulations. Finally, the analysis is accelerated by a factor larger than three orders of magnitude using SVMs instead of MoM-LP.