A phenomenological model of polymer melt spinning is proposed that allows exact analytical treatment. Using the description of crystallite orientation by means of a simple Ising-type approach, it is possible to follow the crystallization and orientation processes up to rather high draw ratios and large times. Approximate solutions for the strain-rate and time dependences of the fibre temperature, degree of crystallinity and orientation are obtained. It is shown that the early stage of crystallization is described by the Avrami equation with exponent 2.