In this paper, the modeling and vibration control problem of a satellite with two flexible solar panels are addressed. Symmetric flexible solar panels attached to the center body are used to represent the dynamics of a flexible satellite system. The left and the right panels are modeled as two Euler-Bernoulli beams, and the main body of the satellite is modeled as a lumped mass in the center of two panels. The single-point control input is applied at the center body to suppress the vibrations of both panels. Based on the construction of a physically motivated Lyapunov function, exponential stability is proved with the proposed control. Both the control design and the stability analysis are based on the original infinite-dimensional dynamic equations. Numerical examples illustrate the effectiveness of the proposed control scheme.