This work presents a methodology for the determination of the optimal support locations for nuclear power plant pipelines. The objective here is to minimize the number of supports taking into account the specific design criteria present in the codes and regulatory guides for these special structures. The stress analysis is performed with a finite element program, KWUROHR, developed by Siemens specifically for the analysis of pipelines. On the tube modeling beam elements are employed. From a preliminary stress analysis performed on a trial structure, the topology optimization problem is formulated. Stresses and displacements, as well as the sensitivity analysis, obtained for this structure are the inputs for the optimization procedure. The solution of the optimization problem is obtained with mathematical programming techniques, more specifically with recursive quadratic programming. Final stresses and deformations are obtained through reanalysis of the optimal structure.