To address the complexity and lack of practical methods for calculating bending moments of cast-in-place cover slabs in slab culverts, the slabs were simplified as one-way slabs with a pair of opposing edges simply supported and the other pair of edges free, and derived theoretical formulas for calculating the bending moments within the slabs under uniformly distributed loads using elastic theory. The accuracy of the theoretical formulas was validated through case studies using finite element software. Various combinations of length, width, and fill heights exist in highway projects, making the use of theoretical formulas for bending moment calculations cumbersome. Therefore, a simple and efficient method for calculating maximum bending moments in both primary and secondary directions is proposed, which can be used for reinforcement design. Three reinforcement recommendations are provided based on engineering practices.