Vibration and acoustic radiation of circular cylindrical shells are hot topics in the structural engineering field. However for a long period, this sort of problems is only limit to classical homogeneous boundary conditions. In this paper, the vibration of a circular cylindrical shell with elastic boundary supports is studied using modified Fourier series method, and the far-field pressure for a baffled shell is calculated by Helmholtz integral equation. Active control of vibration and acoustic radiation are carried out by minimizing structural kinetic energy and radiated acoustic power respectively. The influence of boundary conditions on the active control is investigated throughout several numerical examples. It is shown that the active control of vibration and acoustic for an elastically restrained shell can exhibit unexpected and complicated behaviors.