Formulas are derived for the far-infrared radiation pattern of cylindrical leaky waves propagating on a planar surface. The formulas can be used to predict the radiation pattern of a general class of leaky-wave antennas, consisting of a finite-size source which excites a radially propagating leaky wave on some planar surface. Leaky-wave antennas consisting of antenna elements embedded in dielectric layers (microstrip elements) fall into this category. Using the equivalence principle, formulas are derived for both transverse electric (TE) and transverse magnetic (TM) leaky waves with arbitrary propagation constants. The formulas allow for radiation from cylindrical apertures of arbitrary size, so that the effect of truncating the supporting planar surface with an absorbing material can be determined. Particular attention is devoted to the case of a leaky wave for which the real and imaginary parts of the complex propagation constant are equal, since this type of wave has been shown to be responsible for broadside radiation in certain leaky-wave antennas comprised of dielectric layers. >