Many existing studies on punching shear in a RC flat plate slab without shear reinforcement consider uncracked concrete in the compression zone or the aggregate interlock mechanism in the cracked tension zone as shear resistance to external shear forces. However, recent studies have provided clear experimental evidence indicating interdependency between the resistance mechanisms in uncracked and cracked concretes. This study aims to extend the dual potential capacity model (DPCM) for estimating the punching shear strengths of RC slabs. The proposed model can consider both the shear resistance mechanisms of the compression and tension zones by introducing dual demand curves and corresponding potential capacity curves based on a robust theoretical background. In addition, a simplified method was also developed for a better applicability, and test results collected from existing studies were compared against those estimated from the proposed methods and design code models. Based on a total of 224 punching shear test results, the proposed methods were verified, and their analytical accuracy was also compared with those estimated by design codes. The punching shear strengths estimated by the proposed method agreed well with the test results regardless of key variables. The estimation presented the average and coefficient of variation (COV) of the ratio of calculated to tested strength equal to 1.023 and 17%, and the simplified model showed 0.993 and 15.9%, respectively.