In this work we present a detailed computational study of the structural and elastic properties of cubic Al(x)Ga(y)In(1 - x - y)N alloys in the framework of the Keating valence force field model, for which we perform an accurate parametrization based on state-of-the-art density functional theory calculations. When analysing structural properties, we focus on the concentration dependence of the lattice constant, as well as on the distribution of the nearest and the next nearest neighbour distances. Where possible, we compare our results with experiment and calculations performed within other computational schemes. We also present a detailed study of the elastic constants for Al(x)Ga(y)In(1 - x - y)N alloy over the whole concentration range. Moreover, we include the accurate quadratic parametrization for the dependence of the alloy elastic constants on the composition. Finally, we examine the sensitivity of the obtained results to computational procedures commonly employed in the Keating model for studies of alloys.