By use of an eigenfunction expansion method, the expressions for the properties of kinematics and kinetics, which are due to scattering and radiation for a floating vertical circular cylinder over a coaxial cylindrical barrier in water of finite depth, are derived in the presence of an incident linear waves. The radius of the barrier is larger than or equal to that of the floating vertical circular cylinder. This paper presents the analytical solution for the radiation potentials due to heave, surge, and pitch and for the diffraction potential due to the diffraction of an incident wave acting on the fixed cylinder. It also proposes a set of theoretical added masses, damping coefficients and exciting forces. The results of the expressions are the same as that of the cylinder over a cylindrical barrier, the radius of wich is the same as that of the cylinder, in water of finite depth for added masses, damping coefficients and exciting forces at the same condition. Two methods to calculate exciting forces are presented and the results of the methods are the same. Finally, Analytical results of added masses, damping coefficients and exciting forces are obtained for different size of the barrier.