Direct numerical simulations of compressible, homogeneous, turbulent shear flows are used to evaluate Reynolds stress models. Three pressure-strain models, which are either linear, quadratic, or cubic in the anisotropy tensor are considered. Dilatational dissipation and pressure-strain correlation models do not correctly capture the compressibility effects seen in the direct simulations. In particular, the increase in the anisotropy of normal stresses and the reduction in the shear stress are not reproduced by any of the models. Also, the use of the incompressible form of the dissipation-rate equation to determine the solenoidal part of the dissipation is found to be questionable. Abid, Ridha Unspecified Center NAS1-19299; RTOP 505-70-62-15...