The problem of elastic wave propagation in polycrystals with quasispherical grains is solved by the effective medium method. The general scheme of the method in application to polycrystals is developed. The approximate solution of the homogenization problem based on the perturbation theory (Born approximation) is presented. The phase velocities and attenuation factors of the longitudinal and transversal waves in polycrystals of Al and Zn are obtained. The method predicts physically correct behavior of the mean wave fields in the long wave, stochastic, and diffusive regions. Comparison of the predictions of the effective medium method with experimental data and the Born approximation is presented.