Modern society has become more and more dependent on information services, transferred in both public and private network, than ever before. The use of integration of computers with telecommunications has created a so-called “Information Age”. The advent of high capacity digital telecommunication facilities has made it possible for the huge amount of traffic to be carried in an economical and efficient method, in recent years. These facilities, which are used to carry much higher capacities than the traditional ones, also result in the network’s vulnerability to the failure of network facilities, i.e. a single link failure. This thesis is concerned with the technology by which the spare capacity on the link of mesh networks is placed in order to protect the active traffic from network failure with a minimal cost. Although there have been many works to address the issue all of these works have been developed based on the assumption that the link cost with its capacity is linear. In fact, the linear cost functions does not reflect the reality that optic fiber cables with the specific amount of capacities are only available, in other words, the link cost function is stepwise rather than linear. Therefore, all existing algorithms developed for the linear assumption may not be applicable properly for the stepwise case. A novel heuristic algorithm is proposed to solve the problem in this thesis. The algorithm is composed of two parts as follows. In part one, a maximum flow algorithm is employed to work out the maximal amount of feasible spare paths consisting of spare capacities in the network to re-route the disrupted traffic at the event of network failure. In part two, a newly proposed algorithm is used to find an alternative path on which to place the non-rerouted traffic on the failed link with the minimum network cost increment. The superiority of the algorithm is presented over other algorithms published in this area.