With the Lippman-Schwinger equation, dyadic Green's functions, and the vector coherent transfer function method, an electromagnetic theory of a waveguide multilayered optical memory is first developed for the static case, from which a theory describing a conventional multilayered optical memory with bits stored as a refractive index change is also derived. In addition, the formulas for readout signals and cross talk are given, and some problems of numerical calculations are discussed. The theories can be used effectively for optimum design of a multilayered optical memory with bits stored as a refractive index change.