Loaded tooth contact analysis (LTCA) has always been a significant contact mechanical performance optimization technique for spiral bevel and hypoid gears. To distinguish with the conventional simulated loaded tooth contact analysis (SLTCA) based on economical software package, numerical loaded tooth contact analysis (NLTCA) and its innovative semi-analytical determination approach is developed. In full consideration of tooth flank flexural behavior characteristic, double-curved shell finite element modeling is performed and then improved tooth contact analysis (TCA) is applied for data-driven determination of loaded tooth contact points. Then, in additional to the global boundary condition, the accurate local boundary conditions is also investigated. In particular, local Rayleigh-Ritz method is used to get new semi-analytically tooth compliance determination by considering computational accuracy and efficiency. Furthermore, NLTCA model is established in considerations of the accurate contact point matching, compatibility and equilibrium conditions. Finally, the main NLTCA evaluations including load distribution, loaded contact pattern, loaded contact pressure and distribution, and loaded transmission error in consideration of time-varying meshing characteristics, respectively. The provided numerical instance can verify the proposed methodology.