As a new tool of statistical analysis, Copula is introduced to build reliability model for structural system consisting of identical components, by which the complex feature of failure dependence can be depicted. Aiming at symmetric structure systems, typical failure-dependence mechanism of components is discussed firstly. Considering the failure-dependence mechanism, modeling steps based on Gauss Copula and Archimedean Copulas are put forward, in which the twin stress, components strength are chosen as the basic variables and the safety margins are chosen as the analytic variables. Compared with Gauss Copula, Archimedean Copulas have powerful capability of describing the failure-dependence mechanism owing to the adjustable parameters can be determined according to the rank correlation coefficient and the information about the critical failure point. Archimedean Copula-based reliability models are applicable to non-normal situations. A numerical example is given to show that the new method is reasonable and feasible. Copula-based reliability models can give a new path for reliability analysis of complex systems with failure-dependence.