The tensile behaviour of a commercial grade of isotactic polypropylene was tested in a temperature range between 20 and 150 degrees C with a video-controlled testing system which is capable of imposing a constant true strain-rate within the neck automatically. The results are displayed in the form of effective stress-strain curves and modelled by a constitutive equation in a multiplicative form. It is thus shown that, for each temperature, the plastic response can be described up to very large strains (epsilon similar or equal to 2.0) by a set of four parameters. The assumptions introduced in this modelling are critically discussed in order to check the validity of the simplifying hypotheses (strain homogeneity, isochoric deformation, etc.). The constitutive equation thus obtained was utilized in a finite difference code in order to predict the development of stretching instabilities of polypropylene. The simulation gives access to the engineering stress-strain response of the stretched test piece and to the detailed kinetics of the incipient neck. It is found that the severity of the instabilities is less at room temperature than near the melting point because of the decrease of the strain-hardening and of the strain-rate sensitivity with temperature.