The effect of gamma radiation under vacuum on polypropylene is analysed on the basis of a simple kinetic model. The influence of the irradiation parameters, total absorbed dose and dose rate, on the rates of the main reactions occurring during irradiation, i.e. p-scission, addition to double bonds and termination, is studied. Using kinetic equations, and free radical and double bond balance relationships, we show that it is possible to rationalize the response of polypropylene to gamma radiation. In particular, on the basis of the mathematical solutions of these equations, we obtain the equation of an ’inversion curve’, implicit function of the irradiation parameters, which gives the dose values enhancing chain branching and molecular weight increase at fixed dose rate and vice versa. These ’inversion conditions’ are also found experimentally analysing the rheological behaviour of a commercial polypropylene irradiated under vacuum.