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This paper presents a method of solving Lagrangian version of goving equations that allows boundary conditions at the free surface to be satisfied exactly, which is a three-dimensional generalization of a method first put forward by Stoker. Analytical expressions of nonlinear hydrodynamic pressure up to the third order and of free surface displacement up to the fourth order of an accelerating cylindrical tank were obtained. Here only the motions of objects in their early stage after initial impulses was considered. As a justification of the method, the importment special case when the ratio of tank diameter to fluid depth tends to infinity was taken as an exainple, which shows that the linear hydrodynamic pressure obtained agrees completely with Westergaard or von Karman’s classical result.