We propose a generalized kinetic model for the peroxide initiated modification of polyethylene. It takes into account not only combination reactions but also transfer to polymer and scission. The model describes the length of the polymer chain and the concentration of vinyl groups simultaneously. Any number of vinyl groups per molecule is allowed. The resulting infinite system of mass balance equations is solved using a double moment technique. The model calculates number, weight and z-average molecular weights and the average concentration of vinyl groups as functions of time. The kinetic constants and the initiation efficiency were estimated through a nonlinear regression using experimental data. The relevance of each one of the reactions included in the mechanism was assessed. By means of the model we studied the influence of temperature and initial peroxide concentration on the modified polymer properties. It follows well the observed experimental trends and gives good estimates of both average molecular weights and average vinyl content, within experimental error.