This work is concerned with the formulation, implementation and test of a model for determination of the minimum prestressing force and the optimum tendon profile, to prestressed isostatics and hiperestatics beams. It will be considered in formulation, that the prestressing cable has a development segmented in second grade parabolas, in which the length of each one will be predetermined. In addition, simplifications will be considered with regard to the prestressing force and the prestressing losses. With these assumptions and an artifice of variables change, linear programming problem will be obtained, where the variables will be the prestressing force and the parabolas coefficients that represent the cable geometry. The objective of this linear programming problem will be to minimize the prestressing cost, based on some constraints. These constraints will limit the cable geometry, since this one has to be continue, represented for smooth curves and to be inside of the beam, and will limit the stresses at the top and at the bottom fibers of each studied sections according to Brazilian Codes NBR 8681, NBR 7197 e NBR 7187. Different loads cases will be considered and the studied sections will be predetermined. As project result, we will have an optimum tendon medium profile and the minimum prestressing force P0, where the immediate losses will be included. The formulation implementation was developed in "C" language, ANSI standard, which guarantees that the same code can be compiled in different computers and for different compilers, making the program portability easy. For optimization, the commercial program LINDO- Linear Interactive and Discrete Optimizer was used, which allows interaction with the user, is practical and very efficient. Four examples with different complexity will be tested and studied. From four beams tested, one was presented by Calçada (1993) in his paper "Traçado Óptimo de Cabos de Pré-esforço em Pórticos", and the other ones were designed by engineers in structural design offices. The two design solutions, the one given by the program and the other obtained by the offices, are compared in order to validate both the formulation and the program implemented.