Wave radiation problem in heaving motion from a vertical cylinder of circular cross-section and truncated cylinder of an arbitrary cross-section in the water of finite depth is studied. First, wave radiation from the circular cylinder is summarized which was solved analytically by Yeung (1981). The water domain is divided into two regions: the interior region below the cylinder and the exterior region outside the cylinder. The interior and exterior solutions are matched by the continuity of pressure and normal velocity in both cases. The vertical cylinder of a circular cross-section is solved by using the separation of variables method in cylindrical coordinates. The coeffcients of interior and exterior solutions are related by the matching conditions. The system of equations formed by these unknown coeffcients has been solved. Then, the non-dimensional z component of force is calculated by integrated pressure on the floating body. The real part and imaginary parts of this force give added mass and damping coeffcients in heaving motion, respectively. These numerical results are used for the verification of asymptotic solutions of the present thesis. In the second case of this thesis, we treat wave radiation problems in heaving motion from the non-circular cylinder by using an asymptotic method. The asymptotic method of this thesis was suggested by Dişibüyük et al. (2017). Dişibüyük et al. (2017) suggested the non-dimensional maximum deviation of the cylinder crosssection from a circular one plays the role of a small parameter of the problem. The thirdorder asymptotic solution is used. Unknown coeffcients of interior and exterior potentials are solved by using Fourier coeffcients at each order of approximation. The advantage of the method is that the boundary conditions can be solved for different cross-sections by using the Fourier coeffcients. The results are compared with other numerical results.