This work compares the Deterministic Design Optimization (DDO) with the Reliability-Based Design Optimization (RBDO) of reinforced concrete plane frames. The structure is modeled by a finite element mesh using bar elements and considering both geometric and material nonlinearities. In the formulation of the proposed optimization problem the design variables are defined for each element of the finite element mesh. They are the areas of tensile and compressive reinforcement at the element ends, the depth of the element rectangular cross-section, the areas of shear reinforcement, and the parameter D used to describe the deformation limit sates for the element cross-sections defined according to the Brazilian code for the design of concrete structures NBR 6118 (ABNT, 2004). The optimization algorithms used are the Sequential Linear Programming (SLP), the Sequential Quadratic Programming (SQP) and the Method of Feasible Direction (MFD). The random variables of the RBDO problem are the concrete compressive strength, the steel compressive and tensile strength, as well as some applied loads. The performance functions are of two types, the first relates to the critical load of the structure and the second to the control of displacements in the serviceability state. For performing the calculation of the probability of failure for the associated performing function in each iteration of the RBDO problem, the method FORM (PMA) will be used in connection with the HMV algorithm for obtaining the project point. The sensitivity analyses are carried out by the analytical method.