The binary alloy system MoRu has been studied from first principles with the purpose of calculating the enthalpy of solution in the Ru rich region of the phase diagram. Our approach is based on the exact muffin-tin orbital method and the coherent potential approximation (EMTO-CPA). Further we have extracted effective interatomic interactions by means of the screened generalized perturbation technique (SGPM). The interactions were then used in Monte Carlo simulations of the solid solution energy at elevated temperatures, where the effect of local lattice relaxations was also included. In this way we are able to take into account accurately the effects of short range order on the stability of the solid solution. Our theoretical result indicates that the solid solution is considerably less stable than has been measured experimentally. We note that the difference in energy between bcc and hcp structures of Mo plays an important role in determining the mixing enthalpy. Our results then indicate that a lower value of this difference, such as that claimed by the Calphad community, could bring the theoretical results into closer agreement with experiment.