The main objective of this paper is to construct a robust and reliable metamodel for the mechanized tunnel simulation in computationally expensive applications. To accomplish this, four metamodeling approaches have been implemented and their performance has been systematically evaluated through a comparative study utilizing pure mathematical test functions. These metamodels are quadratic polynomial regression, moving least squares, proper orthogonal decomposition with radial basis functions, and an extended version of the latest approach. This extended version has been proposed by the authors and named proper orthogonal decomposition with extended radial basis functions. After that, a system identification study for mechanized tunneling has been conducted through the back analysis of synthetic measurements. In this study, the best performing metamodel, that is the one suggested by the authors, has been employed to surrogate a complex and computationally expensive 3D finite element simulation of the mechanized tunnel. The obtained results demonstrate that the proposed metamodel can reliably replace the finite element simulation model and drastically reduce the expensive computation time of the back analysis subroutine.