Solid-state extrusion experiments were carried out through constant area convergent-divergent dies using two crystalline polymers, i.e. ultra high molecular weight polyethylene (UHMWPE) and polytetrafluorethylene (PTFE), with the aim of producing extrudates exhibiting biaxial orientation. The evolution of orientation was examined along the extrusion axis by measuring the off-plane birefringence values at various distances from the entry on specimens removed from the dies. Simple analytical expressions relating orientation factor to draw ratio in the three mutually perpendicular directions were derived for crystalline polymers. These generalised relationships were found applicable for all types of deformations, i.e. monoaxial, biaxial and pure shear. On the basis of the data obtained and the predictions from the theoretical analysis, the deformations taking place in dies with small converging angles, known as fish-tail dies, were found to be close to a state of pure shear deformations, while dies with high converging angles initially, then changing to high divergencies in the second section, known as dual-taper dies, were found to give rise to a state of unbalanced biaxial deformations.