A major problem in understanding seismic wave propagation in the seafloor is to distinguish between the loss of energy due to intrinsic attenuation and the loss of energy due to scattering from fine scale heterogeneities and bottom roughness. Energy lost to intrinsic attenuation (heat) disappears entirely from the system. Energy lost to scattering is conserved in the system and can appear in observations as incoherent noise (reverberation, time spread, angle spread) and/or mode converted waves. It has been shown by a number of investigators that the seafloor scattering problem can be addressed by finite difference solutions to the elastic wave equation in the time domain. However previous studies have not considered the role of intrinsic attenuation in the scattering process. In this paper, a formulation is presented which includes the effects of intrinsic attenuation in a two-dimensional finite difference formulation of the elastodynamic equations. The code is stable and yields valid attenuation results.