In the previous paper the authors have derived the functions of the shallow water waves under the condition that the phenomena close to the resonances are to be considered. While, it turned out by example calculations that in some region of frequencies a little away from the resonance, the calculated time dependent variation of the level of water surface during a period of oscillation of the tank is not symmetrical with respect to the middle of the period. This does not seem to be the case. To avoid this unreasonableness, more general conditions which are not confined to the near-resonance are used and symmetric solutions are obtained. Owing to this, moreover, the whole expressions of wave functions have become rather simple and clear. Our results are almost equal to the wave functions of Verhagen and Wijngaarden which are obtained by the method of the characteristic curves for the vicinity of the first resonance, and are similar to Chester's results for the resonant oscillations of gas in closed tubes. For several cases of to, the wave functions are examined numerically and figured.