The paper investigates stochastic polling systems using machine learning. M/M/1 and MAP/M/1-type polling systems with cyclic polling, as well as M/M/1-type polling systems with adaptive cyclic polling are considered. To train a machine model of a M/M/1-type polling system, we used the results of analytical calculations, and for other considered systems that do not allow exact analysis, we used the simulation results. Numerical examples are given, and it is shown that the results of machine learning are close enough to the results of analytical or simulation calculations.