The transmission of ultrasonic waves at oblique incidence through a plane plate made of viscoelastic material is theoretically studied. The absorptive properties of the solid medium which have been neglected in the previous theory are considered. The resulting expression for the transmission is of the same form as in the case of a non-absorptive plate, but the propagation constants of the waves are replaced by complex quantities in the expression. The effect of the absorption is remarkable near the critical angle of incidence for longitudinal or transverse waves in solid. It is shown that when the absorption by the plate is appreciable, the more simple formula can be applied and the formula agrees well with the experimental results described in the next report.