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Oil wells typically have production tubing installed within casing strings. In the scenario of buckling, the casing string is commonly simplified to be rigid at the designing stage (Mitchell, 2012). It hasn't been fully explored by literature yet how the neglected casing string displacement impact the buckling mechanism. An improved analytical model in this paper based on Mitchell's study (2012) addressed this issue in vertical wells. The post-buckling configuration typically includes two scenarios: sinusoidal and helical buckling. This paper investigates both scenarios of concentric tubular buckling and develops an analytical model based on the minimum energy theory. The author has verified the new model with well-recognized literature before the application. Computations are also conducted to investigate the prediction improvement than previous models. This new model can find broad applications in both onshore and offshore completion/production operations. To the knowledge of the authors, there are only two existing models so far for concentric string buckling, namely Christman's model (1976) and Mitchell's model (2012). The authors find by case study that (1) Christman's model tends to overestimate the stiffness of concentric string system. (2) Mitchell assumes an unlikely transition configuration before helical buckling, where the concentric string system is independent of the wellbore. As a result, Mitchell's model ignores the wellbore restraint impact on buckling in the transition mode. The author brought up a sinusoidal buckling model for the concentric strings in the transition mode. The analytical model is derived based on the minimum energy theory. This model can evaluate the buckling induced pitch, bending moment, bending stress and total length change. The author also verified the new model with well-recognized literature by Lubinski (1962). In the end, computations investigate the prediction improvement than previous models. • There is very limited research on concentric tubular buckling regardless of its wide application onshore and offshore. • Christman (1976) overestimates the dual pipe stiffness assuming minimal inner pipe motion and evenly distributed loading. • Mitchell (2012) assumes an unrealistic dual pipe buckling configuration under small buckling force. • This new model addresses the deficiencies and provides a more reliable prediction for practical use. [ABSTRACT FROM AUTHOR]