This paper presents a new method for studying bistatic scattering of acoustic waves by finite cylinders. The method is based on the assumption that a differential element of the cylinder scatters sound as though it were part of an infinite cylinder of the same radius. Under this assumption, the scattering function of cylinder body is derived rigorously using the Kirchhoff integral theorem. The effect of scattering by the ends of finite cylinders is also considered. It is shown that the result from the previous cylinder method [T. K. Stanton, J. Acoust. Sec. Am. 83, 55-63 (1988)] is a special case of the present method. The new approach, particular-useful for calculating the bistatic scattering function, is compared to this previous method by various examples. The numerical computation shows that when the scattering direction is close to the incidence direction, the difference between the two methods is small, and the difference generally increases as the scattering direction moves increasingly away from the incidence direction. It is further shown that the difference between the two methods is more severe for weak scatterers. (C) 1997 Acoustical Society of America.