RY Sct is a unique massive binary star system in a short transitional evolutionary phase. It is an eclipsing binary where both stars have overfilled their Roche cavities, so that the system is in an “overcontact” state. It is surrounded by a young circumstellar nebula. The binary is regarded as a rare progenitor of a type WR+OB system. RY Sct is close to the Eddington luminosity limit, so that radiative pressure plays an important role in mass loss. At least one of the components of the close binary may be associated with a rare class of LBV stars or the so-called S Doradus variables. We have calculated the orbital elements using the old photometric data of Zakirov and Kumsiashvili and new spectral data, together with an analysis of HST observations. A model was examined according to which the components of RY Sct are in an overcontact state and fill their Roche cavities. The brighter primary component transfers mass to the more massive but less bright secondary. The binary system is surrounded by a common envelope. As initial parameters we, chose a mass ratio q = 4.42 and orbital period P = 11d.12471, and used an orbital inclination of i = 75.6°.