Waechter and Philip (1985) obtained the asymptotic expansion of the mean infiltration rate for large s from a buried circular cylinder using a scattering analog. Here s(=&agr;l/2) is defined as the ratio of the characteristic length l of the water supply surface (in fact, its radius) to the sorptive length 2&agr;-1 of the soil and &agr; satisfies the relationship K(&psgr;)=K(0)e&agr;&psgr;, where K is the hydraulic conductivity, and &psgr; is the moisture potential. This exact solution cannot be used directly to obtain the separate contributions to the mean infiltration rate from the top and the bottom halves of the cylinder; our analysis is based on a new class of special functions derived from the modified Bessel equation with a forcing term. In this paper, we obtain the separate asymptotics for the two halves for large s to make a comparison with the results of the trench problem (Waechter and Mandal, 1993). The asymptotic expansions for top and bottom halves are (2/&pgr;)(0.69553s-2/3) and (2/&pgr;)(1+0.30066s-2/3), respectively, whereas for a semicircular trench, the mean infiltration rate is given by (2/&pgr;)(1+0.30066s-2/3). ¿ American Geophysical Union 1993