The numerical solution techique was applied to the equations of the coupled torsion-horizontal vibration of a beam, and the computing program by means of a digital computer was made. Using the above-mentioned program, preliminary calculations were made for the uniform beams, the main result of which is that, in almost of all the case of the uniform beam, the horizontal and the torsional modes of coupled vibration have the same number of nodes. Another result is that the corresponding horizontal and torsional modes can have different number of nodes if the distance between centre of mass and of torsion varies along the length of the beam. The calculation were also made for 4 actual ships and the results were compared with measured ones. For the ships in the present calculation the effect of coupling on the frequency is small and can be neglected for the calculation of lower modes such as excited by reciprocating machinery. Although the errors between computed and measured frequencies are about 10%, the improvement of computing accuracy can be expected by further study on the virtual mass of the water and on the rigidity and the centre of twist of the ship with hatch openings.