The flow of multi-mode differential model fluids through planar and axisymmetric 4:1 contractions is studied numerically and comparison with experimental results is made where possible. The Phan-Thien/Tanner, Giesekus and Modified Upper Convected Maxwell constitutive models are investigated. An efficient algorithm is constructed by employing discontinuous interpolants for the extra stress components and the pressure field. An operator splitting methodology is adopted to extract the advective parts of the constitutive equation. These are solved by application of a time-discontinuous/Galerkin least-squares method. Satisfactory agreement with previous work and experimental results is obtained.