A combination of ab initio total energy calculations with Calphad approach is applied to model the site occupancy and thermodynamic properties of the Fe-Cr, Co-Cr, Fe-V, and Fe-Mo binary sigma-phases as a function of composition and temperature. For each binary sigma-phase the parameters of the model are the ab initio calculated total energies of so-called end-member compounds, which represent all the 25=32 variants of complete occupancy of each of the five crystallographically inequivalent sites by one or the other alloy component. The paramagnetic state of the sigma-phases has been taken into account within the disordered local moment approach. The Fe and Co atoms are found to retain high spin moments when they occupy high-coordination-number sites in the structure. Using our model we were able to reproduce the experimentally observed site occupancy in the FeCr sigma-phase. The calculated site occupancies in the Co-Cr, Fe-V, and Fe-Mo sigma-phases are also presented and discussed.