While there have been a number of numerical and experimental studies to find the hydrodynamic coefficients and wave excitation forces of a floating horizontal circular cylinder, no complete analytical attempt has yet been made to estimate those coefficients and forces. Here, we present the analytical solutions to the problem of a horizontal circular cylinder. Instead of solving the cylinder problem directly, first, we solve the problem of a floating rectangular box analytically. Then, by mapping those solutions into the cylinder problem via Close-fit transformation, we obtain the desired results with a comparison to the existing numerical and experimental results. Regarding the wave excitation force, the analytical results of multipole expansion method are also compared together. Even though the multipole expansion have mostly been studied in numerical way, analytical method is introduced in this paper mathematically. Additionally, results for asymmetrically immersed cases are also presented by a composite function of Close-fit conformal mapping and parallel translation.