The authors perform numerical simulations of mechanical repsonses of two truss structures (tetragonal and Kagomé) subject to compression and shear. Responses of both structures are initially isotropic, but only the Kagomé core maintains the isotropy after yielding, it strain hardens and is resistant to plastic buckling in compression and shear. The tetragonal core is anisotropic in shear with two soft orientations, both governed by the onset of plastic buckling.