Consider the crystal containing a small fraction of vacancies as a homogeneous crystal, and the difference between perfect and imperfect crystal reduces to the modification of the potential function. The relation between the rate of change of the elastic constants, c11 and c12, and concentration of vacancies is derived by the use of a Morse function. Owing to the relaxations of the neighbouring atoms, the effect of the elastic constants on the change of mutual interactions due to vacancy relaxation is taken into account. The first and second nearest-neighbour relaxations for Al are found to be (1.61, -0.32), expressed in percentage of normal distances. The positive sign indicates relaxation toward the vacancy and the negative sign indicates relaxation away from the vacancy. In the case of Cu, it is estimated that 1 per cent vacancy concentration would decrease the elastic constants by 1.3-1.4 per cent. However, the vacancy would have less effect on the elastic constants in Al than in Cu.