In this work, we present a model for spectral transmittance of extrinsic fiber Fabry-Perot cavities using paraxial Gaussian approximation and ray transfer matrices. The finesse is obtained through a Lorentzian fitting of the spectral transmittance derived from the proposed model. The relationship between the finesse and the radius of curvature on both sides of the cavity was analyzed to obtain high finesse. The predictions of the model are found to be in good agreement with the experimental results for the fabricated cavities.