This paper introduces the uniform damping control of flexible spacecraft. The dynamic characteristics of spacecraft are reviewed and a criterion for dynamic performance is described by a uniform damping control approach which exhibits three distinctly attractive features. It is shown that 1) the associated uniform damping control law is independent of the spacecraft stiffness, 2) the associated control forces are proportional to the spacecraft mass density, and 3) the uniform damping control law is decentralized. The uniform damping control solution is shown to represent a first-order approximation to a special globally optimal control problem. Also, the implementation of uniform damping control is considered using discrete (in space) actuation and sensing type devices. Robustness in the presence of errors due to implementing the control using discrete components is characterized.