The intrinsic (maximum observable) birefringence Δnmax at complete orientation of the assembly is determined for polypropylene (PP) and polyethylene (PE) fibres. This is quantified by determination of the molecular orientation parameter of the fibre at a given value of the draw ratio using mathematical expressions. Also, a new approach is suggested for determining the unknown initial value of the draw ratio for given fibres. The double-beam polarizing (Pluta) microscope with a drawing device attached is used for this purpose. Illustrations using microinterferograms, graphs and tables are shown.