Structural integrity of an in-service component containing damage such as corrosion and thermal hot spot has to be evaluated regularly so as to certify the acceptance and safety of continued service of the component. In this paper, limit load solutions of a damaged conical shell, particularly local wall thinning and thermal hot spot, is investigated. The derived solutions are based on identifying the regions in the damaged component that directly participate in the plastic action (kinematically active). The concepts of reference volume and decay length are employed to identify the kinematically active regions in the damaged conical shell. The different solutions proposed in this paper are compared with the elastic-plastic finite element analysis. The results indicate that proposed solutions can be used with acceptable accuracy to make integrity assessment decisions.