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In this study, a novel inverse design method, called Elastic Surface Algorithm (ESA), is proposed for airfoil shape design in subsonic and transonic flow regimes. ESA is a physically based iterative inverse design method that uses a flow solver to estimate the pressure distribution on the solid structure, i.e. airfoil, and a 2D solid beam finite element code to calculate the deflections due to the difference between the calculated and target pressure distribution. The proposed method is validated through the inverse design of five different airfoils. In addition, three design examples in subsonic and transonic regimes are presented to prove the effectiveness and robustness of the method. Finally, the convergence rate of the method is compared with MGM and BSA methods. The results of this study showed that not only the ESA method is an effective method for inverse design of airfoils, but also it can considerably increase the convergence rate in transonic flow regimes. [ABSTRACT FROM AUTHOR]