A theory for multifilamentary pattern formation in semiconductors with an S-shaped negative conductivity (SNDC) is presented. The theory is based on the basic equations in electrodynamics and the impact ionization mechanism with double impurity trap levels, which is widely accepted as the mechanism for SNDC. No extra physical quantities and/or parameters are introduced in the theory. The steady-state of the dynamical equations is a one-dimensional reaction-diffusion type equation, which provides stable multifilamentary pattern structures. The stability analysis for the steady-state N-filament (N=2, 3, and 4) solution is given.