When an acoustic plane wave is incident on an elastic plate, energy propagates within the plate, as well as being reflected from and transmitted through the plate. The present study determines the structural intensity as a function of incident angle at different depths along the cross section. It is found that most peaks, but not all, in the structural intensity may be identified as free waves of the fluid–plate system yielding a form of “numerical spectroscopy.” It is also found that for particular frequencies and angles of incidence the direction of the structural intensity parallel to the plane of the plate is opposite than what would normally be expected. Various studies are performed to gain physical insight into this phenomenon.