As a thin-walled, highly deformable precision component, the flexspline is subjected to complex stresses during operation. The fixture is crucial for the manufacturing of the flexspline, requiring a rational structure to ensure manufacturing precision. In this study, a finite element model of a flexspline fixture was established to analyze the contact pressure and strain between the flexspline, expansion sleeve, and core shaft. By utilizing orthogonal experiments and simulations, the maximum contact pressure between the flexspline and the expansion sleeve P_fmax, the maximum contact pressure between the expansion sleeve and the core shaft P_emax, and the maximum strain ε_fmax of the flexspline were obtained under varying pulling force F, taper angle α, and the number of clamps S. Range analysis was conducted to investigate the impact of F, α, and S on P_fmax, P_emax, and ε_fmax. These findings provide valuable references for designing and optimizing harmonic drive flexspline fixtures.