<p>In this paper, we first present a stochastic model for the survivable capacitated network design problem, in which the demand vector is uncertain. To deal with the uncertainty of the demand vector, we use the joint chance-constrained programming method. According to the real-world application, it is assumed that only partial distribution information of uncertain demand, such as support, mean, and variance is available, and we use a robust method to deal with this uncertainty. The obtained robust counterpart model is a distributionally robust joint chance-constrained model. Due to the intractability of the distributionally robust joint chance-constrained model, we use the deterministic and Bonferroni approximation methods to solve it. The obtained models from the first and second methods are mixed integer non-linear programming (MINLP) and mixed integer linear programming (MILP), respectively. We propose an iterative approximation optimization method to provide the lower and upper bounds for the MINLP model. In the end, the efficiency of the proposed techniques is evaluated by some realistically sized instances.</p>