The ultrasonic attenuation in imperfect insulating crystals is calculated by the method of thermodynamic Green's functions. It is assumed that imperfections change the temperature dependence of the ultrasonic attenuation by modifying the frequency and lifetime of thermal phonons which are coupled to the ultrasonic wave by anharmonic interactions. The resulting expression, valid for all Ωτ, can be reduced with certain assumptions to a simple functional form. For longitudinal sound waves, the expression reduces to essentially the Akhieser expression in the limit Ωτ≪1 and to an expression obtained by Maris in the limit Ωτ≫1. τ, however includes the effects of imperfection damping as well as anharmonic damping of the thermal phonons. At low temperatures (Ωτ≫1), the addition of imperfections increases the attenuation since the thermal phonon lifetime is reduced, thereby relaxing energy conservation. At high temperatures (Ωτ≪1), the addition of imperfections decreases the attenuation, allowing the thermal phonons to relax more rapidly to the instantaneous equilibrium phonon distribution. The condition determining the point of crossover for the imperfect and perfect crystal attenuation curves is derived, and the crossover is shown to occur near Ωτ=1 for small imperfection density. The connection between these results and Bömmel and Dransfeld's data for neutron irradiated quartz is investigated.