Solid state processing is a very efficient method of introducing molecular orientation in polymeric products. In this respect, die-drawing of polymers has received considerable attention as it allows to achieve very high draw ratios in comparison to free-axial drawing. In this work, square billets were drawn through dies made up of four axially symmetrical sections to form convergent channels with spiralling walls. The materials studied were high density polyethylene (HDPE) and quenched (amorphous) polyethylene terephthalate (PET) to produce filamentary products with draw ratios up to 9:1. The results have shown that the rotational components of the deformations resulting from the spiralling walls, which are superimposed onto axial extensions, alter the balance between tensile and shear stresses acting on the material in passing through the die. This has considerable effect on the drawing forces and properties of the final products. Noteworthy is the relative amount of free-axial drawing in the longitudinal direction, and associated elastic recovery, which cause substantial differences in the overall draw ratio imposed on to the filaments. This effect is particularly pronounced for PET. At the same time the spiralling walls of dies reduce the overall level of orientation in the amorphous phase and brings about an increased resistance to splitting under transverse compression and a reduction in shrinkage at higher temperatures.