The present paper deals with the weight minimization of tubular trusses subjected to multiple loads under size, stress and buckling constraints. The applied optimization procedure is based on a virtual strain energy density approach developed by the first two authors, already tested in plane and space truss structures. The key point of the method is the activation of at least one of the imposed displacement constraints. In case where such limitations are absent, a dummy displacement constraint is introduced instead, which iteratively sustains corrections until convergence is achieved within the desirable tolerance. The efficiency and practicability of the proposed method was tested in typical cases of tubular truss structures. For reasons of comparison, the same cases were also optimized using Sequential Quadratic Programming (SQP), which is a powerful mathematical programming optimization method. The results revealed that the proposed method performs very well in terms of convergence, of required number of iterations and of optimum tracing, while the value of the introduced dummy displacement constraint has insignificant effect on the optimization procedure.