With a view to calculating depolarization and differential attenuation of microwaves by rain, with allowance for the variable shape and orientation of raindrops, the theory of P. C. Waterman is applied to the calculation of cross sections and depolarization ratios of spheroids, and drops of the shapes determined by H. R. Pruppacher and R. L. Pitter. Use of Waterman's extended boundary condition facilitates computation. The scattering characteristics of spheroids appear similar in nature to those of spheres, in the regimes considered. Marked singularities in the characteristics of backscattering depolarization appear at optical size 1.5. The Pruppacher and Pitter drops scatter similarly to equivalent oblate spheroids. Implications for weather radar measurements are briefly discussed.