A theoretical and experimental study of multiple beam Fringes of Equal Tangential Inclination (FETI) formed with two concentric spherical surfaces have been performed. Systems of concentric circles in transmission and at reflection for two concentric convex or concave spherical surfaces were recorded. The path difference between any two successive interfering beams to produce real or virtual fringe system in transmission or at reflection has been derived. It has been proved that this path difference is exactly the same in case of two convex or concave concentric spherical surfaces, also in case of transmission or at reflection. The fringe localization has been critically studied. Expressions for the surfaces of localizations of the systems of multiple beam interference fringes in transmission and at reflection in case of (a) two convex, (b) two concave concentric spherical surfaces have been derived. The effects of changing the radii of curvatures, the interferometer gap and the refractive index on the shape of the surfaces of localization have been theoretically studied. Application of FETI to provide useful information about the parameters of the spherical surfaces and the enclosed media have been presented.