In the flat formulation of the problem, a formula is derived for the transverse force acting from the side of the Karman vortex path on the cylinder. It is shown that the multi-frequency transverse force has the shape of a meander and depends on the main parameters of the vortex track. In the problem of transverse vibrations of the thread, a solution is given for multi-frequency and harmonic flow effects. When deriving the formula, the current function for a system of vortices in the plane is used. The transverse force is determined by integrating the change in the amount of motion along the contour covering a part of the formed vortex path of the Karman with a length – the distance between the centers of vortices of the same level. The formula for the transverse force can be useful for analyzing and calculating self-oscillations that occur during the transverse flow of long structures: threads, cables and pipes.