The wurtzite InxGa1-xAs (x = 0.5) alloys are studied by numerical simulation based on first-principles calculations. The results indicate that the band gap bowing parameters obtained with the equilibrium lattice constant. As a precursor to obtaining the band offsets, the electronic band structure of InGaAs was calculated for different compositions. These results are analysed and compared with experiment. The method generally used in the literature for determining the elastic constant tensors (Cij) of alloys usually consists in simple linear combination of those of the constituent components. From such results it can be deduced that the method generally used for calculating the ternary alloys' Cij by linear combination of those of its binary components could be inexact, because the requirement of linearity of the elastic constant behaviour is not fulfilled. We also present elastic constant tensors.