Commercial cellular solids such as metal foams and honeycombs exhibit deformation and failure responses that are dependent on specimen size during testing. For foams, this size dependence originates from the fabrication-induced material and structural inhomogeneities, which cause the uncontrolled localization of deformation during the testing of foam cubes. Different peak loads and failure modes are observed in honeycomb specimens in the plate-shear configuration depending on specimen height. This size dependence causes difficulty in obtaining a more representative constitutive behavior of the material. It has recently been established that the size dependence under uniaxial compression can be eliminated with tapered cellular specimens, which enable controlled deformation at a given region of the specimen. This concept is extended in this paper to the biaxial testing of butterfly-shaped cellular specimens in the Arcan apparatus, which focuses deformation at the central section of the specimen. The Arcan apparatus has been modified such that all displacements at the boundaries of the specimen could be controlled during testing. As a consequence of this fully displacement controlled Arcan apparatus, a force perpendicular to that applied by the standard universal testing machine is generated and becomes significant. Thus, an additional load cell is integrated on the apparatus to measure this load. Example responses of butterfly-shaped specimens composed of aluminum alloy honeycomb, aluminum alloy foam and hybrid stainless-steel assembly are presented to illustrate the capabilities of this new testing method.