A type of leaky-wave antenna that is particularly suitable for applications in the millimeter-wave range is carefully analyzed. The structure is basically a version of the dielectric inset waveguide and the leakage is induced by loading the air-dielectric interface with a photo-etched, periodic, metal-strip grating. The antenna is mechanically simple to realize so that it is particularly suitable for millimeter-wave applications. The aim of the paper is to provide a practical and accurate theory for the design of this class of antennas. The analysis procedure is based on the development of a novel, multimode transverse equivalent network representation. All mutual coupling effects are rigorously taken into account. A simple dispersion relation is derived via a transverse resonance procedure and the complex dispersion behavior of the antenna is obtained through its numerical solution. Useful approximate initial design formulas are given and a detailed parametric analysis is carried out clearly showing the effects of changes of all the structural parameters. The results obtained indicate that the structure, in addition to being mechanically simple to realize, exhibits a very flexible electrical behavior. The theory developed, therefore, is a very powerful tool for the design and optimization of this class of antennas; a very promising candidate for millimeter-wave applications.