Аннотация:A method for determination of double-star-system parameters from observations of shallow partial eclipses by the secondary star or an opaque disk lying in the orbital plane is developed. Analytic expressions for the parameters of shallow eclipses and corrections for the inclination angle for tidally distorted stars are obtained for a system having a circular orbit and consisting of two spherical stars or a spherical star and a circular disk lying or not lying in the orbital plane. The validity limits of the shallow eclipse approach are analysed. Analytic results are compared with numerical calculations. In the case of Cyg X-1, the limits for the radii and masses of the components and some other system parameters are found from parameters of the light curve depression, provided that this depression observed near orbital phase 180\deg is caused by eclipses.