<p>The Multiple Corrugated Diaphragm(MCD) couplings, as a new type of flexible coupling, exhibit complex non-axisymmetric mechanical characteristics under angular loads due to their sinusoidal corrugated structure, posing challenges to traditional analytical methods. This paper aims to establish an efficient analytical model based on plate and shell theory to predict the stress distribution and angular stiffness of the MCD under angular loads. The study combines analytical methods with the finite element method (ANSYS), segments the corrugations, and establishes reasonable boundary conditions to derive analytical formulas for the deflection curve, stress distribution, and stiffness calculation at the maximum deformation section. The results show that the analytical model calculations are highly consistent with finite element simulations: the deflection curves follow similar trends, the stress distribution patterns generally match, and the angular stiffness calculation error is within 7%. The findings indicate that the established analytical model effectively captures the core mechanical behavior of the MCD, providing a reliable theoretical basis for the rapid design and optimization of high-performance MCD Couplings.</p>