IN THIS PAPER WE CALCULATED THE ELASTIC CONSTANTS OF G-CE. THE CALCULATIONS WERE PERFORMED SELF-CONSISTENTLY USING THE FULL POTENTIAL AUGMENTED PLANE WAVE PLUS LOCAL ORBITAL (FP-APW+LO) METHOD. WE USED THE GENERALIZED GRADIENT APPROXIMATION (GGA) TO CALCULATE THE EXCHANGE-CORRELATION ENERGY. THE ELASTIC CONSTANTS WERE OBTAINED FROM THE SECOND ORDER DERIVATIVES OF ENERGY WITH RESPECT TO LATTICE PARAMETERS. IN THIS WORK WE INTRODUCED A METHOD TO IMPOSE A DEFORMATION TO THE PRIMARY STRUCTURE TO SIMPLIFY OUR CALCULATIONS CHANGING AN FCC STRUCTURE TO BCT.