Research on the acoustic design sensitivity is significant for its ability to provide the optimized orientation for low noise design of radiating structures. In this paper, analytic equations are presented for acoustic sensitivity analysis of cylindrical radiators based on the spatial Fourier transform, by which the sensitivity of acoustic quantities with respect to the design variables such as structural parameters or physical properties can be calculated. Because of the use of spatial Fourier transform, the proposed method has high computational efficiency. The validity is verified by the numerical simulation of infinite and finite cylinders.