In the survivability and simplicity aspect, SONET Self-healing Ring(SHR) is one of the most important schemes for the high-speed telecommunication networks. Since the ring capacity requirement is defined by the largest STS-1 cross-section in the ring, load balancing is the key issue in the design of SONET SHR. Recently, most of the research on load balancing problem have been concentrated on the SONET single-ring case. However, in certain applications, multiple-ring configuration is necessary because of the geographical limitations or the need for extra bandwidth. In this thesis, the load balancing problem for SONET dual-ring is considered. Two models are examined: a SONET dual-ring only with inter-ring demands and the one with inter- and intra-ring demands. Symmetric demand pattern is assumed for both cases. A SONET sigle-ring network with asymmetric demand pattern is also examined. We present a linear programming based formulation of each problem. Computational experiments are performed on various size of networks with randomly generated demand sets.