In this paper a numerical method is presented to determine drag and l i ft forces on circular cylinders by model ing the unsteady flow field characterized by vortex shedding. The results of the computations are compared with experimental data obtained from a special verification test program. In the Sections 2 and 3 the numerical method based on the scheme proposed by Chorin, using a Lagrangian description of the flow field, is discussed in detail. Special attention has been paid to the accuracy and numerical efficiency of the method. In Section 4 an interesting formulation is given for the forces exerted on the cylinder by the vortex shedding process. This method is useful especially for vortex methods where the pressure is unknown. The experimental set-up is discussed in Section 5, while the results of computations and tests are compared in Section 6. Both the general character of the flow field and the drag and lift force time histories are considered.