Abstract: Based on the thought of seeking problem-solving approaches in practice, an effective and simple method was previously presented which is used for back-analysis of the elastoplastic displacement of a circular tunnel. In this paper, the method is promoted to the gate arch-shaped tunnel applying the complex function theory, and rationality and uniqueness of its strength parameters are discussed. First, using the elastic solutions of deformation in such tunnels, the authors prove a conclusion that the ratio of arch vertical displacement over side-wall horizontal displacement is independent of Young's modulus, and an elastic back-analysis theory is formulated. Then, we point out that the criteria of elastic parameters from back-analysis is unreasonable since analysis values are compared with measured values at the same ratios of vaults and side walls. An improved criteria is derived by the stress release rules, and the uniqueness of strength parameters is discussed from the view of mathematics. Finally, application in a case study of an actual project verifies the applicability and reliability of the promoted back-analysis method. This study would improve the applicability of geotechnical back-analysis to actual projects.