Underwater sound scattering from objects without shear stress has been treated using the finite-difference method in the time domain [S. Wang, J. Acoust. Soc. Am. 99, 1924–1931 (1996)]. In many realistic targets, however, both longitudinal and transverse waves exist. In order to deal with scattering from such objects, a set of FDTD expressions are established based on Hooke’s law. For a 3-D problem, these include six difference equations for stress and three for particle velocity. The expressions reduce to the previously obtained form consisting of four equations (one for sound pressure and three for velocity) if shear wave is absent. On the interface between the water and the solid scatterer, the boundary condition is satisfied by introducing two compliance coefficients which are the averages of compressive compliance and shear compliance of the two media, respectively. Shear compliance is set to infinity both in the water and on the boundary. Thus the FDTD iteration can be done in a unified manner in both media as well as on the boundary. Numerical results for sound fields around and inside an aluminum bar submerged in sea water and insonified by a plane wave are presented. [Work supported by NNSFC.]