Reasonable strength criterion is of vital importance in the elastic-plastic analysis of surrounding rock of circular tunnel using power hardening-ideal plastic model. In the aim of obtaining a strength criterion suitable for the power hardening-ideal plastic model, first of all the four commonly used strength criteria for geotechnical materials were summarized; the unified linear equation of plane strain was acquired; then the unified solutions of stress, displacement and plastic zone radius of circular tunnel's surrounding rock in plastic zone and power hardening zone in the presence of seepage were deduced; and finally the theoretical strength effect, power hardening parameters, and pore water pressure on the elastic-plastic analysis of circular tunnel's surrounding rock were discussed. Research results revealed outstanding theoretical strength effect. Comparison with finite element analysis results suggest that Mogi-Coulomb criterion, unified strength theory with parameters b=1/2 and c=0, unified strength theory with parameters b=1 and c=0 are favorable; inscribed circle DP2 criterion and equivalent area circle DP4 criterion could follow in sequence; DP3 criterion and Mohr-Coulomb criterion are not recommended; circumscribed circle DP1 criterion and unified strength theory with parameters b=1 and c=1 should be used with caution. Among the power hardening parameters, the power hardening coefficient m had no impact on the radius of plastic zone, but the plastic zone displacement increased with the reduction of m; the plastic zone radius and displacement of surrounding rock both swelled with the growth of power hardening index n. The plastic zone radius, radial stress and tangential stress augmented with the climbing of pore water pressure. The research results offer an important theoretical basis for the support design of circular tunnel's surrounding rock with strong strain hardening effect.