As a pressure pulse propogates through a randomly layered, lossless fluid medium, it experiences an apparent attenuation due to pulse broadening by interbed multiples. This attenuation increases as the impedance contrast between layers is increased, for example, by making the angle of incidence more oblique. In elastic media, P-S coupling affects the partitioning of energy between the interbed multiples and therefore leads to a different amount of apparent attenuation than the fluid case. In elastic media, both the impedance contrast and the amount of P-S coupling increase as the angle of incidence is made more oblique. We explore the effect on apparent attenuation through numerical simulations. We find that: 1) the attenuation of the elastic P wave increases more slowly than the fluid P wave as the angle of incidence is made more oblique; 2) The attenuation of the elastic S wave decreases by a factor of about 2 as the angle of incidence is made more oblique; and 3) The coherent S wave pulse experiences a small (1%) apparent increase in propagation velocity.