In many branches of the “Ship-hydrodynamics”, the fields concerning the interaction among a hull, a propeller and a rudder have many unsolved problems. The author has specially interested in the problems concerning a rudder, and so had reported the measured results of the twisting moment acting upon the actual ship's rudder-stock, in 1953. However, the phenomenon appeared in the experiments of the actual vessels were very complicated and difficult to solve. So that, the author had promised further investigations by model experiments. The author, recently, had a chance for this further investigation to carry, as a result of the completion of the model experimental equipments, water circulating channel, and planned the general research of ship's rudder from the hydrodynamical standpoint. This first report treats theoretically the effect of the angular velocity of steering on the performance of an open rudder. From the results of theoretical calculation of the non-uniform vortex theory, the author finds as follows : - 1. The twisting moment acting upon a rudder-stock grows larger than the values at steady state, by the effect of the angular velocity of steering. 2. The lift can be divided into two parts at this unsteady state. One of them acting on the point behind a quarter of the chord-length of the rudder from its leading edge, and the other acting on the middle point of the rudder. 3. The lift, which acts on the quarter point, is a function of angular velocity and helm angle, but the other lift, which acts on the middle point, is a function of angular velocity only. 4. The growing-up tendency of a twisting moment in affected seriously by the position of the centre of the rudder-stock. In the case of general merchant vessels, this increment of twisting moment gets larger accompanied to increasing of distance of the centre of rudder-stock from the leading edge.