The paper describes the development of an analytical response model of an extrinsic fiber Fabry – Perot interferometer with a multilayer cavity in case of spectral interrogation. The system of equations allowing to calculate the spectral characteristic S(λ) of such interferometer has been derived under assumption of a single reflection from each of the layer surfaces. Moreover, the key parameters of the interferometer, namely, the layer refractive indices, the reflections of coatings, the layer thicknesses and the light loss in layers were taken into account as well. The light propagation inside the interferometer cavity was analyzed in terms of the Gaussian beam model. The features of the frequency analysis of the S(λ) oscillations were also considered. As an example, the obtained equations were used for evaluation of a two-layer extrinsic fiber Fabry – Perot interferometer design.