This paper presents a risk-based approach to resilient network design. The basic design problem considered is that given a working network and a fixed budget, how best to allocate the budget for deploying a survivability technique in different parts of the network based on managing the risk. The term risk measures two related quantities: the likelihood of failure or attack, and the amount of damage caused by the failure or attack. Various designs with different risk-based design objectives are considered, for example, minimizing the expected damage, minimizing the maximum damage, and minimizing a measure of the variability of damage that could occur in the network. A design methodology for the proposed risk-based survivable network design approach is presented within an optimization model framework. Numerical results and analysis illustrating the different risk based designs and the tradeoffs among the schemes are presented.