A deformable mirror is the core component of an adaptive optics system, its ability to correct is affected by many factors, and its design process is a multidimensional variable optimization problem. The existing design methods for deformable mirrors require repeated iterations over a long period, and the efficiency is low, making it difficult to adapt to the increasing demand for the development efficiency of deformable mirrors. To solve the abovementioned problems, this paper proposes a new design method for deformable mirrors that combines a genetic algorithm and an elastic mechanics influence function analysis model to significantly increase the design efficiency of deformable mirrors and realize rapid design of deformable mirrors. Based on the proposed method, the structural parameters of the defocus and astigmatism-corrected deformed mirror are designed. The results show that the method successfully optimizes the convergence of 11 variables over 100 iterations, significantly reducing the number of individual calculations and allowing for the rapid design of deformable mirrors.