The nonlinear goal programming approach is used for solving multiobjective optimization problems. When the goals are vague and somewhat imprecise the model can be transformed in a fuzzy nonlinear goal program. It is shown how the model accomodates various aggregation forms of the multiple objectives, including simple or squared, weighted or unweighted additive functions. New in this field is a preemptive priority model which is maybe not very universal but will prove of valuable help in appropriate cases. The approach is illustrated with two extensively developed examples of structural optimization, which reveal the usefulness of the methodology. This paper is certainly worthwhile studying for any practitioner facing similar problems of structural and mechanical systems.