Extending the approach proposed by Cole and Schieve (1995 Phys. Rev. A 52 4405) for a one-dimensional cavity with one moving mirror, we develop a geometrical method to solve exactly the generalized Moore (GM)equations for a one-dimensional cavity with two moving mirrors. As examples of applying our method, the GM equations are solved in detail when the two mirrors oscillate resonantly, and the dependences of the solutions on the frequency and dephasing of the mirror motions are investigated.