A functional integral method for performing the statistical averages implicit in problems involving multiple scattering is developed. The scattering fields in a noncrystalline medium are represented as a fixed set of fields for each incident particle, but are assumed to vary randomly from one particle in the beam to the next. The method is applied to eikonal treatments of both multiple scattering and photon radiation. This latter problem involves the Landau-Pomeranchuk-Migdal effect, and correction terms to earlier treatments are evaluated. {copyright} {ital 1997} {ital The American Physical Society}