A path-flow formulation of defining MPLS FRR bypass LSPs is presented. The path-flow formulation comprises first identifying a set of candidate bypass LSPs, each of which meets various network constraints and has an explicit route around a network facility to be protected. The constraints may include Quality of Service (QoS) guarantees, implementation requirements, network element resource limitations, and resiliency requirements. The constraints may be user-selected, and may be non-linear. The set of candidate bypass LSPs form a linear programming (LP) problem, or an integer linear programming (ILP) problem if the allowable number of bypass LSPs is constrained. In an optimization step, LP solutions are used to select the bypass LSPs from among the candidate bypass LSPs by allocating bandwidth to them.