Аннотация:A problem from the class of unsteady plane flows of an incompressible ideal fluid with a free boundary is considered. A conformal mapping of the exterior of a unit circle onto the region occupied by the fluid is sought. The solution is constructed in the form of power series with respect to time, which are analytically continued with the use of Padé approximants and a change of variables of a certain special type. The free boundary shape and the pressure and velocity distributions are found.