Creep of cyclically loaded thin shells of revolution and their fracture due to creep and fatigue mechanisms are studied. Creep-damage equations for steels and nickel-based alloys are built by the use of scalar damage parameter. Constitutive equations were derived using the method of asymptotic expansions and averaging over a period of cyclic loading. The cases of fast and slow varying of temperature and loading are regarded. General problem statement and method for solution of creep problems at cyclic loading are presented. Strain-stress state in shell structures is determined by the use of homemade FEM creep-damage code, where the finite element of conical shell is used. Results of creep-damage problem for conical panel are discussed.