The behaviour of planar Newtonian and Non-Newtonian polymeric jets is investigated in the context of injection mould filling. The incompressible Stokes flow model consistent with the application of injection mould filling is described together with the shear rate dependent fluid viscosity for a typical polymeric melt. The numerical procedure for the solution of the nonlinear system is briefly discussed as well as the mesh generation and the melt front tracking algorithms employed. In the analysis, the buckling behaviour of Newtonian and Non-Newtonian jets are firstly compared. There after the behaviour of Newtonian jets are analysed for various values of the aspect ratio in an attempt to study the validity of the Cruikshank buckling conditions for planar Newtonian jets. It is argued that the Reynolds number of highly viscous polymeric melts is relatively low and the aspect ratio condition is the critical condition dictating the buckling behaviour. Finally, an aspect ratio design criteria is established for buckling-free and folding-free flow of polymeric jets.