Work continues on efforts to elucidate the flow characteristics of viscoelastic fluids through complex geometries, using experimental results coupled with detailed mathematical models. The research examines the problems caused when elastic effects are comparable to or greater than viscous effects. Flow through a sudden contraction and flow around a sphere are analyzed with a two-color laser-Doppler velocimeter. This project is the first successful effort to model such non-Newtonian fluid flow that incorporates shear and elongation in the finite difference numerical solutions.