In this paper, we explore the possibility of applying the moment metho
d to determine the electromagnetic field distributions inside three-di
mensional bounded nonlinear dielectric objects of arbitrary shapes. Th
e moment method has usually been employed to solve linear scattering p
roblems. We start with an integral equation formulation, and derive a
nonlinear system of algebraic equations that allows us to obtain an ap
proximate solution for the harmonic vector components of the electric
field. Preliminary results of some numerical simulations are reported.