As a key component of industrial robots, the study of the dynamic characteristics of harmonic gear reducers and the determination of resonance positions are of significant importance. To avoid the occurrence of resonance problems in the operation of harmonic gear reducers, this study conducted modal analysis and harmonic response analysis on the harmonic gear reducer. Particularly, considering that the flexible wheel is the part of the reducer most likely to fail, it is the key component of vibration analysis. Here, we selected the SHG-25100 harmonic gear reducer as the research object and constructed its three-dimensional model under load as well as the finite element analysis model after the cam assembly bearing deformation. Considering its periodic input characteristics, the finite element method was used to conduct harmonic response analysis under constant torque. The acceleration response curve of the flexible wheel and rigid wheel contact surface in the x, y, and z directions, as well as key dynamic parameters such as natural frequency and response amplitude, were successfully obtained. The results indicate that the reducer exhibits significant vibration in the y direction at the resonance frequency of 95.5 Hz, and vibration in the x and y directions at the resonance frequencies of 40 Hz and 45 Hz respectively. When operating the reducer, these resonance frequencies should be avoided.