We present the details and the derivation of density-functional-based expressions for the total energy and pressure for random substitutional alloys (RSA) using the Korringa-Kohn-Rostoker Green’s-function approach in combination with the coherent-potential approximation (CPA) to treat the configurational averaging. This includes algebraic cancellation of various electronic core contributions to the total energy and pressure, as in ordered-solid muffin-tin-potential calculations. Thus, within the CPA, total-energy and pressure calculations for RSA have the same foundation and have been found to have the same accuracy as those obtained in similar calculations for ordered solids. Results of our calculations for the impurity formation energy, and for the bulk moduli, the lattice parameters, and the energy of mixing as a function of concentration in fcc CucZn1−c alloys show that this generalized density-functional theory will be useful in studying alloy phase stability.