Using the exact muffin-tin orbital (EMTO) method in combination with the coherent potential approximation (CPA), we studied the influence of alloying elements Al, V, Zr, Tc, Re and Ir on the phase stability, lattice parameters, densities, and elastic properties of NbMoTaWMx (M = Al, V, Zr, Tc, Re, Ir; 0 ≤ x ≤ 1.0) refractory high entropy alloys. The predicted lattice parameter and elastic parameters agree with the available experimental and theoretical data. We calculated the atomic size difference (δ), the valence electron concentration (VEC) and the total energy of face-centered cubic (fcc), body-centered cubic (bcc) and hexagonal closed-pack (hcp) structures. We found that all studied NbMoTaWMx (M = Al, V, Zr, Tc, Re, Ir; 0 ≤ x ≤ 1.0) systems have the bcc structure. We showed that Al and Ir decrease the stability of the bcc structure and Zr significantly enlarges the lattice parameter of the host. Vanadium increases the ductility of NbMoTaW system. On the other hand, Al and Ir have strongly non-linear effect on the ductility, with clear minimum at x = 0.55. The present results provide consistent theoretical data and call for experimental investigation for these alloys.