The saddle-shaped magnet, due to its unique nonplanar structure, requires different analytical techniques from those used for conventional high-temperature superconducting (HTS) magnets. When conducting experiments to evaluate the performance of the saddle-shaped magnet after construction, the measurable electromagnetic parameters mainly include voltage, critical current, and magnetic field distribution. To reproduce these parameters through analysis, an appropriate analytical model is required, but such a model has not been sufficiently developed in the past. In this study, a distributed circuit model was developed to analyze the voltage and current distribution within the saddle-shaped magnet. A numerical method was proposed to quickly calculate the inductance required when applying the distributed circuit. Additionally, the precise critical current estimation problem, which has been considered a challenge for HTS magnets, was solved using the distributed circuit approach. We also analyzed the magnetic field generated by the saddle-shaped magnet and conducted calculations for the harmonic coefficient, which significantly affects the characteristics of the actual beam. A method was developed to assess the impact of screening currents and ferroshim on the harmonic coefficient. Meanwhile, in the mechanical analysis of the saddle-shaped magnet, the key issue lies in the bending strain at the magnet’s ends. Since the well-known constant perimeter winding technique cannot be directly applied to actual windings, a practical solution is suggested. Furthermore, a mechanical analysis model was developed to address the operational characteristics of the magnet.