The digitized Green's function (DGF) algorithm and the underlying theory are described. This finite element algorithm models dielectric particles of arbitrary shape and arbitrary optical structure. DGF predictions of differential and total cross sections are compared with predictions of Mie and EBCM algorithms for several homogeneous spheres and spheroids. Results of tests of convergence of the DGF calculation as the number of elements are increased are presented. Computer time and storage requirements as functions of wavelength and particle size, shape, and optical structure are discussed.