A systematic quantitative method for the selection of models for the high-conversion free radical polymerization exhibiting gel and glass effects has been developed. Four representative models were selected from the literature and were compared on the basis of the same experimental data. All models describe the isothermal time-conversion data over the entire conversion range for a single type and loading of initiator well. Models that are not considering the effect of molecular weight of the polymers on the diffusion of macro radicals fail to describe the time-conversion data if the concentration of the initiator varies at the same time. By simultaneous fitting of the conversion and polymerization degree data it was shown that the Marten-Hamielec model and its extended form (Panke-Stickler-Hamielec model) were not able to describe the number average polymerization degree Pn at the final conversion, where the glass effect occurs. This occurred because both models neglect the change of the radical efficiency f in this region, which has more effect on Pn than the change of the propagation rate coefficient (see part II of this series).