The evolution of networks in telecommunications has brought on the importance of design techniques to obtain survivable and cost-effective transportation networks. In this thesis, we study Synchronous Digital Hierarchy (SDH) ring design problem with an interconnected multi-ring architecture overlaid over an optical mesh network. We decouple the problem into two sub-problems: the first problem is the SDH ring selection, and the second problem is the mapping of these rings onto the physical mesh topology. In this structure, the logical topology consists of SDH Add/Drop Multiplexers (ADMs) and Digital Cross-Connects (DXCs), and the physical topology consists of Optical Cross-Connects (OXCs). The ring selection problem is to choose the rings that give minimum inter-ring traffic in the network. Since inter-ring traffic increases the network cost and complexity, we aim to minimize the inter-ring traffic. We propose a greedy heuristic algorithm for this problem that finds a solution subject to the constraint that the number of nodes on each ring is limited. Numerical results on the ring design problem are presented for different topologies. Once the logical topology is obtained, resilient mapping of SDH rings onto the mesh physical topology is formulated as a Mixed Integer Linear Programming (MILP) problem. In order to guarantee proper operation of SDH ring protection against all single failures, each link on an SDH ring must be mapped onto a lightpath which is link and node disjoint from all other lightpaths comprising the same ring. The objective of this mapping is to minimize the total fiber cost in the network. We also apply a post-processing algorithm to eliminate redundant rings. The postprocessing algorithm is very useful to reduce the cost. We evaluate the performance of our design algorithm for different networks.