Abstract: We introduce a nonparametric Plateau problem with partial free boundary on a given plane. The setting we consider is the generalization of a problem arising from the analysis of the relaxed area functional in codimension 2. We discuss the relationship between the relaxation of the area and the Plateau problem. THen we focus on the latter question and show that under suitable hypotheses the solution is also a solution of the classical parametric Plateau problem with partial free boundary on a plane. This research is done in collaboration with Roberta Marziani and Giovanni Bellettini.