The velocity potentioal due to a pulsating source, the so-called Green function for periodic oscillation of water, in a rectangular canal is obtained by using a new method. This potential is important, for example, to discuss the effect of the wave reflection by the tank wall when experimenting a ship model in a rectangular tank. The main characteristics of water waves in a canal are that there exist resonant frequencies, and that the system of progressive waves for a frequency consists of a finite number of component waves with different wave lengths. When the ratio of the breadth 2 l of the canal and the wave length λ, of the progressive wave due to the pulsating source, for the horizontally unbounded case satisfies 0<2 l /λ<0.5, the progressive wave becomes a two-dimensional sinusoidal wave with the wave length λ. When 0.5<2 l /λ, the wave system involves component waves with the wave length longer than λ. The numerical calculations are conducted, and the examples are shown in § 6.