For the people interested in the behaviors of a floating body in waves, exact nonlinear calculations of a 3-D body of arbitrary geometry in arbitrary waves must be the final goal. In order to achieve the purpose, we, in this paper, limit our attention to a 2-D body problem in arbitrary (non-breaking) waves in an inviscid and irrotational fluid. In an inviscid and irrotational fluid, it is well known that a velocity potential exists. Using the velocity potential, the equations to be solved are reduced to a single Laplace equation plus 6 equations of motions of a body and thus our computational burden is greatly reduced. However, it is hard to extend a potential theory to a body-motion in a viscous fluid, which is our final goal. Therefore we dare to avoid the use of a velocity potential and solve the continuity equation written in terms of the velocity and the Euler's equation of motions of water particles, so that the future extension to a viscous fluid problem can be carried out without total reformulation of a numerical scheme. In this paper, we first compare a numerically produced regular wave train of small amplitude with analytical solutions. Secondly, we compare the response amplitude operator of a body in small regular waves calculated by the present method with those measured in experiments as well as with the linear potential theory. Next we compare the time history of the motion of a body in transient waves of large height with that measured in experiments. Lastly, we present results of bi-harmonic motions caused by a nonlinear restoring moment.