In this paper, modeling and vibration control of flexible solar array paddles with revolute joints, which are mounted on satellites and free flying robots, are discussed. We consider flexible solar array paddles which are in zero gravity field and are rotated about two axes of the flexible plates by motors. We assume the solar array paddles can be regarded as connected two fully clamped rectangular plates. We first derive partial differential equations and two sets of boundary conditions which represent vibration of the paddles and ordinary differential equations which represent the dynamics of angles of rotation of motors. On the basis of a finite-dimensional modal model for the distributed parameter system, an optimal controller with low-pass property and a robust H∞ controller are constructed. Simulation results confirm that the controllers perform remarkably well.