Summary: This work is focused on the analysis of the survivable capacitated network design problem. This problem can be stated as follows: Given a supply network with point-to-point traffic demands, specific survivability requirements, a set of available capacity ranges and their corresponding discrete costs for each arc, find minimum cost capacity expansions such that these demands can be met even if a network component fails. Solving this problem consists of selecting the links and their capacity, as well as the routings for each demand in every failure situation. This type of problem can be shown to be NP-hard. A new linear mixed-integer mathematical programming formulation is presented. An effective solution procedure based on Lagrangean relaxation is developed. Comparison heuristics and improvement heuristics are also described. Computational results using these procedures on different sizes of randomly generated networks are reported.