We report here the development of a theory for the parameter regime between two well understood limits, that described by single scattering theories commonly used for backscattered ultrasound, and a fully diffuse limit in which the ultrasound has scattered many times. A radiative transfer equation is given describing diffuse ultrasonic intensity as a function of position, time, direction, and polarization. The equation includes the effects of propagation, attenuation, absorption, scattering and mode conversion. Results on backscattered intensity for a simple application are presented. It is anticipated that this approach may be applicable to materials characterization by means of the study of the time, space, frequency, and angular dependence of multiply scattered ultrasound in a variety of elastic media with microstructure.