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The objective of present research is to study the effect of different specimen dimensions on the modulus of rigidity, yield shear stress and ultimate shear stress for AISI 1020 steel and Al T6 6061. The experiments are conducted with key specimen dimensions such as total length, outer diameter, inner diameter, useful length and fillet radius at different levels for solid and hollow specimens. The Taguchi parameter design and optimization approach is used for Design of Experiment and subsequently to predict sets of optimal parameters. The Grey Relational Analysis (GRA) method has been used for multi-objective optimization.