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A model is presented fro the multiply scattered incoherent field in a continuous polycrystalline elastic medium. Unlike a previous development based upon energy conservation considerations [J. A. Turner and R.L. Weaver, J. Acoust. Soc. Am. 93, 2312 (A) (1993)] for a medium containing discrete random scatterers, the present model has been developed from the wave equation and first principles. Appropriate ensemble averaging of the wave equation leads to Dyson and Bethe-Salpeter equations which govern the mean Green’s function and the covariance of the Green’s function, respectively. These equations are expanded for weak heterogeneity and equations of radiative transfer are obtained. The result is valid for attenuations that are small compared with a wave number: α/k«1. Polarization effects are included, as before, through five elastodynamic Stokes parameters, one longitudinal and four shear. The theory is applied to a statistically homogenous and statistically isotropic half-space composed of cubic crystallites illuminated by a plane wave. Results for the angular dependence of backscattered intensity are presented. It is anticipated that this approach may be applicable to microstructural characterization through the study of the time, space, ultrasonic frequency, and angular dependence of multiply scattered ultrasound in elastic media.