Based on the yield criteria of second-order parabola, a refined translational model for punching failure has been developed, assuming that the critical ultimate state is characterized by cracking of the compression concrete on the punching cone and simultaneous splitting of the tension concrete at longitudinal-rebar level. An upper-bound solution was obtained and a general one was developed under arbitrary-order parabola yield criteria. Moreover, the deduced complex model was simplified for better practice. The statistical results, with a collection of 231 specimens, show that for the proposed curved-generatrix model, the coefficient of variation for the prediction-to-observation ratios(i.e.,0.201) is much less than that for the straight-generatrix model previously proposed(i.e.,0.250). In addition, it is slightly lower than that for the current GB code(i.e.,0.202), and its mean(i.e.,0.940) is obviously superior over the latter(0.799).