A method has been developed for calculating the fluence and dose perturbations which occur in the shadow of inhomogeneous structures exposed to beams of charged particles. It is shown that differences in scattering power in adjacent portions of irradiated material can give rise to fluence perturbations which, in turn, are responsible for dose perturbations. A quantitative analysis of this process is developed which permits calculation of both the perturbed primary fluence and dose distributions. Results of these calculations are given for a square-faced edge discontinuity. The analytic technique, however, can be applied to more complicated interfaces and the general formulae are developed in this paper. They include provisions for the important modifying effects of beam divergence, of overlying or underlying homogeneous material, and of nonuniform beam profiles. In a companion paper, more complex geometries are analyzed and comparisons between calculations and experiments are presented.