We have developed a unified approach to solve for the attenuation and phase velocity variations of elastic waves in single‐phase, polycrystalline media due to scattering. Our approach is a perturbation method applicable for any material whose single‐crystal anisotropy is not large, regardless of texture, grain elongation, or multiple scattering. It accurately accounts for the anisotropy of the individual grains. It is valid for time‐harmonic waves with all ratios of grain size to wavelength. It uses an autocorrelation function to characterize the geometry of the grains, and thereby avoids coherent artifacts that occur if the grains are assumed to have symmetrical shapes and suggests new methods for characterizing distributions of grains that are irregularly shaped. We have carried out numerical calculations for materials that are untextured and equiaxed, and have cubic‐symmetry grains and an inverse exponential spatial autocorrelation function. These calculations agree with the previous calculations which are valid in the Rayleigh, stochastic, and geometric regions, and show the transitions between these regions. The complex transition between the Rayleigh and stochastic regions for longitudinal waves, and the severe limitations of the stochastic region for grains with fairly large anisotropy are of particular interest.