In this paper,a beam-column design problem is formu-lated into an optimization problem The modern optimization technique,sequential unconstrained minimization technique(SUMT),is used toselect the design vesiables at points.The optimum designs obtained arereasonable and verifiable.This procedure may be used in the design ofbeam-columns.Considerable savings can be achieved due to the effectiveuse of material through the best proportion of the shape of beamcolumns.