The macroscopic geometric shape of a hyper-redundant manipulator can be described by a curve which is called the reference or backbone curve (BBC). In this paper, a discrete model with compliance is developed for the BBC that is a practical approximation to a continuous elastic cord. Based on the proposed model, kinematic redundancy is resolved through shape optimization: minimizing the elastic potential energy of the BBC. The formulation introduced here is general and can be efficiently used for the configuration control of hyper-redundant manipulators. Moreover, the proposed discrete model is well suited for a class of variable-geometry-truss (VGT) manipulators that are made up of double-octahedral modules. The effectiveness of the model is verified by numerical simulations and hardware experiments.