Uniqueness research is one of the basic theories of displacement back analysis. The displacement analytic solution of a deep circular tunnel in transversely isotropic rock mass is deduced firstly; and then the uniqueness of displacement back analysis of a circular tunnel in transversely isotropic rock mass is discussed by means of identifiability conditions. The results indicate: all of 6 parameters can't be determined simultaneously no matter how many the measuring points are set; only when there are at least 3 known parameters

may the other parameters be determined simultaneously; whether the vertical ground stress component is equal to the horizontal one has obvious influence on the results；in the aspect of identifiability

two ground stress components have the best effect

elastic modulus and Poisson ratio on the isotropic plane take the second place

and elastic modulus and Poisson ratio in the direction vertical to the isotropic plane have the worst effect.