To study the influence of the principal stress rotation on the relaxed soil pressure of tunnels, based on the trajectory of the major principal stress arches, the lateral pressure coefficients under the tower-shaped (triangular) and basin-shaped sliding failure surfaces were analyzed for common project scenarios in actual engineering projects. The lateral pressure coefficient calculation formulas considering the principal stress rotation angle were proposed. According to the force balance of the soil micro-element in the limit equilibrium state, the calculation formula of the relaxed soil pressure at the tunnel crown was derived. Compared with the relaxed soil pressure calculation formula of Terzaghi, the proposed formula for calculating relaxed soil pressure does not contain the soil lateral pressure coefficient, which has multiple influencing factors and tends to be challenging to accurately calculate, and instead substitutes it with the principal stress rotation angle which has a significant impact on the relaxed soil pressure and is closely related to the engineering construction and soil properties. This is especially true for cohesive soils when compared to existing formulas. For relaxed soil pressure, the proposed formula does not require using iterative methods and coordinate translation to calculate the lateral pressure coefficient, thereby improving computational efficiency and accuracy. The case study results demonstrate that the algorithm presented in this paper is significantly superior to Terzaghi’s approach, with estimated values aligning well with experimental measurements.