We have developed an analytical technique for synthesizing a leaky-wave antenna in the form of an irregular hollow rectangular metal waveguide with a narrow wall in the form of an array of circular metal cylinders using an approximate expression for the reflection coefficient of a plane wave from a fine-periodic lattice of circular metal cylinders and the dispersion equation for a waveguide with a partially transparent wall. As an example of the application of this technique, two leaky-wave antennas are synthesized: with a uniform and sinusoidal distribution of the field amplitude along the antenna. We have performed electrodynamic modeling of synthesized antennas using the finite element method. For a synthesized antenna with a uniform amplitude distribution, the results of a numerical experiment are compared with the results of measurements of an experimental sample in the centimeter wavelength range.