The article considers motion of a solid body in an unbounded vortex-free flow of an ideal incompressible fluid. Motion of the fluid unperturbed by the body is assumed to be nonstationary and to have velocity gradients. The force on the body from the fluid is determined under the assumption that the dimensions of the body are substantially less than the characteristic dimensions of the flow. Additional masses, not encountered in the case of motion of a body in a motionless fluid. These masses are calculated for a body shaped like an ellipsoid of revolution.