This paper describes a new method to calculate the lateral hydrodynamic forces acting on a ship during manoeuvring motions. On the slender body assumption, the fluid motion around a three dimensional body is approximated by unsteady two dimensional flow in a space-fixed plane normal to the longitudinal axis of the body. Consequently, the hydrodynamic lateral forces acting on the slender body is obtained through integrating two dimensional lateral force over the whole length of the body. The two dimensional flow in infinite region is substituted by that in finite region bounded by an artificial open-boundary on which Sommerfeld's radiation condition is imposed. Making use of Orlanski's method to deal with Sommerfeld's radiation condition, two dimensional Laplace equation is solved by Boundary Element Method and Finite Differences Method, and then two dimensional hydrodynamic lateral force is calculated by differentiating the fluid momentum with respect to time. As an application of the method described above, the hydrodynamic lateral forces acting on a flat plate with aspect ratio equal to 0.2 are calculated and compared with the experimental results. In consequence, it is shown that the stability derivatives predicted by the present method agree well with those measured at oblique towing, CMT, and PMM tests, and that the predicted stability derivatives of a flat plate with aspect ratio equal to 0.05 are in good agreement with the stability derivatives measured by a Series 60 model with a realistic hull form.