SCORIM (shear controlled orientation in injection moulding) is a new technology using pairs of reciprocating pistons connected to the runner system to impose shear in the mould during the holding and packing stages; this provides important control over part properties. A computer simulation is set up, and solved numerically to assist with development and exploitation of this novel process. The one-dimensional transient model considers the cooling and solidification of polymer melt, contained between infinite plane parallel plates, whilst subjected to reciprocating shear flow. A non-Newtonian, temperature-dependent viscosity is used, together with temperature-dependent thermal properties and latent heat of solidification. Two operating modes are considered: (1) flow driven by a fixed pressure gradient; (2) an initially fixed flowrate, which falls after a limiting pressure gradient is reached. Results are shown, based on data for a moulding grade polypropylene; these include details of temperature and velocity fields, pressure and flowrate profiles, and frozen-in material strains, which are related to material alignment. In mode (1) operation, flowrate falls rapidly as solidification proceeds. This is not hindered significantly by viscous heating. Frozen-in strain has its maximum value close to the wall, and falls in a series of oscillations to zero on the central plane. In mode (2), if the limiting pressure gradient is too high, viscous heating can prevent cooling, leading to a dynamic thermal equilibrium. In other cases, where cooling is completed, frozen-in strain can show a complex, oscillatory profile, corresponding to a layered structure in the moulding with alternating regions of higher and lower alignment.