Elastic properties of Gold (Au) are calculated based on Ab Initio approach by which total energy of Au in respect with volume can be obtained. The elastic properties can then be determined by fitting the calculation results with particular parametric formula. Compared with experimental data (macroscopic properties), it is found that the use of Local Density Approximation (LDA) as exchange-correlation functional in calculation produce good results than Generalized Gradient Approximation (GGA) based. Hence, Ab Initio approach is potential to predict elastic properties of solid. However, the exchange-correlation functional should be chosen with great care. This calculation approach is useful for multi-scale simulation which link the result from micro-macroscopic properties and vice versa where engineering can benefit from such a framework.