Two approaches which describe the Weissenberg effect (height profile of a non-Newtonian fluid between rotating vertical concentric cylinders) are discussed. The first is based on an earlier calculation with theological properties of a simple liquid obtained from nonequilibrium molecular dynamics (NEMD). The calculation is redone here using new results on the density dependence of the normal pressure differences. The NEMD calculations are restricted to Couette flow, but describe specifically, in a consistent manner, the effects of finite compressibility. The pressure, viscosity, and normal pressure differences are all found from NEMD to be sensitive functions of density, which requires that the equations of motion be solved iteratively and self-consistently, and a sample calculation is presented for the soft sphere fluid. The second approach is that of Joseph and Fosdick. Their assumptions and techniques are examined and compared with the NEMD calculations.