Abstract: This paper deals with the problem of visoelastic stress analysis of circular tunnels,The finer and surrounding rock of the tunnel are considered to be viscoelastic materials.Taking the dead wight of the surrounding rock as external load,a general viscoelastic solution to the displacements and internal forces of the liner and surronding rock is given, The method proposed to obtain the general solution consists of three steps.First,the liner and surrounding rock are separated from each other,and the radial torce P₀（θ,t）and tangential force t₀（θ,t）acting upon to each other between the liner and surrounding rock are presented in triangular series.Taking consideration of the liner and surrounding rock as elastic bodies,an elastic solution to the displacements and internal forces of the liner and surrounding rock is obtained by elasticity method.Secondly,the viscoelastic solution to the displacements and internal forces of the liner and surrounding rock is obtained from the elastic solution having been found in the first step by the correspondance principle of viscoelastic-elastic.Finally,by using the deformation compatibility conditions between the liner and surrornding rock,the coefficients in triangular series of P₀（θ,t）and t₀（θ,t）are de-termined,and subseqently by Laplace Transform Inversion the wanted viscoelastic solution in physical space to the displacements and internal forces of the liner and surrounding rock is deduced.At the end of the paper an illustrative exmple is given.