In the aerospace industry, thin-webbed gears are preferred for achieving high power density transmission. However, thin-webbed structures always lead to out-of-plane resonance during the transmission process, which commonly happens in helical gears manifesting as violent vibration at specific rotational speed. To address that, a shaft-web-ring dynamic model suitable for helical gear pairs is proposed. The shaft, gear web, and gear ring are modeled based on Timoshenko straight beam, Mindlin plate, and Timoshenko beam theory, respectively. Simultaneously, the potential energy caused by the time-varying meshing stiffness is coupled to the gear ring. The kinetic and potential energies of each discretized finite element of the components are derived based on elastic deformation theory, and the governing equations of each element are obtained using Hamilton’s principle. The model is numerically verified through comparison with modal experiment. The effects of the web thickness and helix angle on dynamic response and stress are studied, revealing that gear web elasticity and an appropriately high helix angle can effectively reduce vibrations at the support bearing, prevent excessive vibrations, and contribute to vibration and noise reduction in the transmission system.