Lattice structures have ranges of thermo-mechanical properties that suggest their implementation in ultralight structures, as well as for impact/blast amelioration systems and heat dissipation media. Considering that proper anisotropy of structure could increase load efficiency, two kinds of 2-D lattice materials designable in specific stiffness and strength of arbitrary direction have been brought forward: variational thickness cell and variational direction cell. The mechanical properties of variational thickness Kagome cell have been analyzed, including effective elastic modulus, yield strength and elastic buckling strength in arbitrary directions. Since the shear buckling of 2-D lattice materials is an important collapse mode especially when relative densities are low, shear buckling strength of various 2-D lattice materials have also been calculated. It is found that compared with the diamond cell, the variational thickness Kagome cell of thickness ratio, m=0.5, possesses the same elastic modulus and yield surface, and higher buckling strength.