Electromagnetic wave radiation from multiple circumferential slots on a conducting circular cylinder is theoretically investigated, The Fourier transform/series technique is used to represent the continuous and discrete modes of the scattered field. The mode matching is utilized to constitute a set of simultaneous equations for the discrete modal coefficients. The residue calculus is applied to transform the scattered-field integral representations into fast converging series forms, thereby facilitating the numerical computations. Numerical computations illustrate the behavior of radiation in terms of the slot geometry, the incident mode, and the operating frequency.