The paper gives the solution of the volcanic islands slope geometry problem which has been obtained within the scope of a mathematical model developed on the basis of the hypothesis by G. F. Becker. The latter assumed volcanoes to be bodies of equal strength (resistance). The suggested equations describe the volcanic constructions profiles as a function of their height, crater's radius and the volcanic rock properties. The computer calculations results were used to construct theoretical contours of volcanic islands. Possible causes of terrace formation on the islands slopes are also discussed, as well as conditions of collapse caldera formation.