Uncertainties associated with random variables, such as, the material proprieties and loads, are inherent to the design of structures. These uncertainties are traditionally taken into account in the project before the design by defining design values for the random variables. The design values of the random variables are obtained from statistical properties of the random variables and from partial safety factors. Once these values are defined the variables are treated as deterministic variables in the design process. This approach has been followed in the conventional design optimization and in many design codes such as the Brazilian code for the design of steel and concrete structures. This simple approach, however, does not allow an estimate of the structural reliability of the resulting project which may have a low (unsafe structure) or a very high (expensive structure) reliability. To overcome this problem a reliability analysis must be incorporated into the traditional design optimization. Design optimization, incorporating reliability analyses, has been denoted Reliability-Based Design Optimization (RBDO). In RBDO, the constraints are defined in terms of the probabilities of failure associated with some prescribed failure functions and therefore, it requires, as in the reliability analysis, the definition of the random variables and information about their statistical properties. In this work, RBDO is applied to the shape and sizing optimization of spatial trusses considering geometric nonlinearities. The constraints considered in the RBDO problem are related to the following failure mechanisms: to the global collapse (limit load), to local buckling and yield stress and to serviceability conditions (displacement bounds). The algorithms used for solving the optimization problem and for performing the reliability analysis are described.