AbstractRecent progress in the simulation of polymeric flows of two key problems in the injection moulding process, carried out by a team at Cornell University, is briefly described. For the filling of cooled thin cavities, the fluid is characterized by a power‐law viscosity with exponential temperature dependence, and interaction between the transient thermal boundary‐layer and the core flow in a domain with moving boundary is essential. The earlier procedure of Hieber and Shen is modified in two aspects: a boundary‐integral formulation replaces the finite‐element treatment of the pressure, and an ‘energy integral’ approach is used for the transient temperature. The second problem is the steady visco‐elastic flow in the juncture region where sudden changes of the geometry and large strain rates occur. The constitutive equation is postulated according to the Leonov model. The main features in the numerical implementation are: integration along a streamline to determine the elastic deformation tensors for a given velocity field, and finite‐element treatment (in time‐dependent form) of the pressure and fields for given stresses. In an example where the contraction ratio is 7:1, results for nominal Deborah number exceeding 100 show no numerical instability. (However, for this problem, the true Weissenberg number, i.e. the ratio of local first‐normal‐stress difference to shear stress turns out to be generally O(10).) The predictions also correlate very well with experimental birefringence measurements.