Using EMTO method we have calculated the total energy of disordered alloys of Ir – Os system. The lattice parameter obtained for fcc and hcp alloys changes very slowly with increasing concentration of Os because the lattice parameters of Ir and Os are close. Calculations performed in the local density approximation (LDA) give slightly lower results compared with the experiment, but the theoretical values and the experimental data agree well with each other. The bulk moduli depend on the composition of alloys and increase with increasing osmium content. The discrepancy between the calculated and experimental values of B0 is less than 10%, which is a typical error for first-principles calculations, the accuracy of which depends on the type of exchange-correlation potential used. The experiment demonstrated that the fcc alloy Ir80Os20 does not undergo structural transformations at pressures up to 55 GPa, but the pressure dependence of the compressibility has a singularity at 20 GPa. It has been suggested that this feature may be due to the occurrence of the electronic topological transition under the pressure. To check the possibility of this we have calculated the Fermi surface for this alloy at different pressures. However our results show the absence of electronic topological transition in this alloy under pressure.