In this paper we study the problem of survivable network design (SND). The problem can be stated as follows: Given a set of nodes, possible edges and costs for each edge and the number of permitted node or edge failures between each pair of nodes, we want to design a cost effective communications network which has the property that there is at least one communication route present between all the communicating node pairs, even in the case of node or link failure. We present the formulation of the problem and present a solution technique based on a constraint addition approach. We decompose the problem into smaller problems that are computationally not difficult to solve. We use the solutions of these smaller problems to generate new constraints that are added to the overall design problem. This iterative procedure is able to solve the survivable network design problem very efficiently. Extensive computational results show the effectiveness of our solution procedure.