The purpose of this paper is to deconvolve the beam pattern effect from the amplitude distribution of sonar echoes from fish to determine the scattering processes at fish. The paper is a continuation of our acoustic methods to measure fish abundance. It demonstrates a direct procedure for determining the fish density (fish/m3), the probability density function (PDF) of scattering processes at fish, and the PDF of echoes. The procedure uses nonoverlapping echoes from a single transducer sonar system. The integral equation for the echo PDF is in Clay and Medwin [AcousticalOceanography(Wiley, New York, 1977), pp. 476–482]. It relates the PDFs of the sonar outputwE(e), transducer beamwT(b), and scattering process at the fishwF(e). I use the transformationsb=exp(−x) ande=e0 exp(−y) to change the integral to the standard form of the convolution integral. The derivation of expressions of the convolution and deconvolution usingztransformations follow directly. We use a ‘‘home‐style’’ microcomputer for computations. Tests of the deconvolution technique on fish echo PDFs for Lake Michigan alewife show the presence of the alewife (10–12 cm length) and an unidentified group of larger fish having two to three times the length of the alewife. Deconvolution of Lake Superior data for 1978 indicate the presence of smelt and an unknown group of larger fish. Deconvolution of 1979 Lake Superior data gives an echo PDF that can be attributed to smelt. In both lakes, fish density estimates are between 10−4and 10−3fish/m3.