The Partial Element Equivalent Circuit (PEEC) method is a powerful electromagnetic modeling and analysis tool capable of converting complex electromagnetic field problems into circuit problems, demonstrating broad application prospects. The calculation of discretized element parameters constitutes one of the key technologies in the PEEC method. To address this, this paper investigates semi-analytical calculation methods for partial inductance within the PEEC framework. The research first employs an iterative algorithm based on Bartky transformation to calculate the inductance of toroidal fundamental elements. Subsequently, the self- and mutual inductance of rectangular fundamental elements are studied, where a normalized geometric parameter approach is introduced to simplify complex integral expressions, making them suitable for computer-aided semi-analytical computation. The accuracy and efficiency of the proposed semi-analytical method are validated using the Finite Element Method (FEM) for both element types through comparative analysis. Building upon the partial inductance calculations, the PEEC method is further applied to compute the impedance of rails. Comparative results with FEM simulations confirm the feasibility and effectiveness of the PEEC approach based on semi-analytical inductance calculations. This work paves the way for extending PEEC applications to broader domains.