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In this paper, we predicted the possible mechanical properties and presented the electronic structure of Zr(3)Al(3)C(5) by means of first-principles pseudopotential total energy method. The equation of state, elastic parameters (including the full set of second order elastic coefficients, bulk and shear moduli, Young's moduli, and Poisson's ratio), and ideal tensile and shear strengths are reported and compared with those of the binary compound ZrC. Furthermore, the bond relaxation and bond breaking under tensile and shear deformation from elasticity to structural instability are illustrated. Because shear induced bond breaking occurs inside the NaCl-type ZrC(x) slabs, the ternary carbide is expected to have high hardness and strength, which are related to structural instability under shear deformation, similar to the binary carbide. In addition, mechanical properties are interpreted by analyzing the electronic structure and chemical bonding characteristics accompanying deformation paths. Based on the present results, Zr(3)Al(3)C(5) is predicted to be useful as a hard ceramic for high temperature applications.