An elastic cylinder, circular in section and infinite in length, is considered in an infinite acoustic fluid. The object of this paper is the determination of the reflected and diffracted pressure fields at large distances resulting from a plane step wave of pressure impinging on the cylinder and moving in a direction normal to the axis of the cylinder. A formal solution is obtained for the general case of an elastic cylinder. Numerical results are computed for rigid, fixed cylinders, and for rigid, floating cylinders. Two different methods are used to achieve results in the different ranges of time which are of interest. A short time approximation is developed by the use of a double integral-transform method. A mode approach and a single integral transform are used for later times. The results show that the reflected pulse decays quickly, within a time on the order of the transit time of the original wave across the cylinder.