We propose and develop a method of solving the problem of exciting ship waves by a submerged object that moves in a non-viscous fluid at a variable velocity. The case of the flush ball moving at constant velocity parallel to the surface of the liquid is considered to validate the proposed method by comparing the results with data reported earlier by other authors. Asymptotic expressions are derived describing the elevation of the liquid surface in the limit of small and large values of the Froude number. The exact solution is represented as two summands, each of them being reduced to one-dimensional integral. One summand describes the “Bernoulli hump”, and another - the “Kelvin wedge.”