Within the framework of the exact muffin-tin orbitals (EMTO) theory we have developed a new method to calculate the total energy for random substitutional alloys. The problem of disorder is treated within the coherent potential approximation (CPA), and the total energy is obtained using the full charge density (FCD) technique. The FCD-EMTO-CPA method is suitable for determination of energy changes due to anisotropic lattice distortions in random alloys. In particular, we calculate the elastic constants of the Cu-rich face centered cubic Cu-Zn alloys ( alpha-brass) and optimize the c/a ratio for the hexagonal Zn-rich alloys for both the epsilon and eta phases.