The stress compensation method (SCM) for shakedown and limit analysis was previously proposed and applied to elastic-perfectly plastic (EPP) piping elbows. In this paper, the SCM is extended to account for limited kinematic hardening (KH) material model based on the extended Melan’s static shakedown theorem using a two-surface model defined by two hardening parameters: initial yield strength and ultimate yield strength. To validate the extended SCM, a numerical test on a cylinder pipe is performed. The results agree well with ones from literature. Then the extended SCM is applied to the shakedown and limit analysis of KH piping elbows subjected to inner pressure and cyclic bending moments. Various loading combinations are investigated to create the shakedown limit and plastic limit load interaction curves. The effects of the material hardening, angle of the elbow and loading conditions on the shakedown limit and plastic limit load interaction curves are presented and analysed. The present method is incorporated in the commercial software of Abaqus and can be considered as a general computational tool for shakedown analysis of KH engineering structures. The obtained results provide a useful information for the structural design and integrity assessment of practical piping elbows.