Microwave brightness temperatures emerging from horizonally finite clouds of hydrometeors have been computed by means of an analytical model. The analytical model is sufficiently fast that simulations of multifarious aspects of this problem can be easily evaluated. The results of these computations were compared with the results of Monte Carlo simulations, and the agreement was found to be satisfactory. The results of the present computations show that radiation emerging from the sides of isolated hydrometeor clouds causes the brightness temperature of such clouds to differ markedly from the brightness temperature of plane parallel clouds. If, however, the effect of the underlying surface is included in the computations of upwelling radiances, then the microwave brightness temperatures of finite clouds depart somewhat less from the plane parallel cloud results. Radiances emerging from hydrometeor clouds over land are less sensitive to the effects of horizontally finite geometry than the radiances emerging from comparable clouds over water. The effect of the finite field of view of satellite-borne microwave radiometers on measured brighness temperatures is considered; it is shown that ambiguities of the order of a factor of 2 in the inferred mean rainfall rate can occur if a rain cloud does not fill the radiometer field of view.