The initial stage of unsteady two-dimensional flow caused by the impulsive horizontal motion of a floating circular cylinder is investigated by using methods of asymptotic analysis. Initially the cylinder is half-submerged and the liquid free surface is flat and horizontal. The liquid is of infinite depth. Then the cylinder suddenly starts to move horizontally with a speed given as a function of time. The liquid is assumed ideal and incompressible and its flow potential. The initial flow is provided by pressure-impulse theory, with an account of a possible separation of the liquid free surface from the trailing face of the rigid surface of the cylinder. The initial position of the separation point on the surface of the moving body is determined by using the condition that the fluid velocity is finite at the separation point (Kutta condition). The motion of the separation point along the surface of the cylinder is numerically determined with the help of the second-order outer solution of the problem and the Kutta condition at the moving separation point. It is shown that the length of the wetted part of the cylinder surface increases at a rate proportional to the speed of the cylinder. The speed of the separation point depends on the Froude number. The pressure on the wetted part of the cylinder can be below the atmospheric pressure for relatively high speed.