An analysis into the factor β in Todd's formula for estimation of the two-node natural frequencies of the flexural hull vibrations are carried out by the calculations of the characteristic values. of the flexural vibration of a beam with such distributions of mass as both cases of light and full load conditions of modern tankers and cargo ships in the vertical and the horizontal transverse vibrations. For estimation of the natural frequencies of the two-node flexural vibrations of tankers and cargo ships by the use of Todd's formula in early stage of hull design, the ratios of the factor β in full load condition to that, in the light condition are presented with various displacement ratios. The normal modes of the vibrations in various cases mentioned above are also presented in the last paragraph of the present paper.