In recent years, significant progress has been achieved in the study of the anisotropy of elastic properties of nonstoichiometric cubic carbides MC_y (M = Ti, Zr, Hf, Nb, Ta) and monoxides MO_y (M = Ti, Nb). The composition of nonstoichiometric cubic compounds MX_y (X = C, O) determines their electronic structure, mechanical (elastic) properties and possible fields of application in modern engineering. This critical review summarizes recent achievements in the semi-empirical evaluation of elastic characteristics of nonstoichiometric cubic compounds. The main results on the dependences of elastic constants c_ij on the composition of disordered nonstoichiometric cubic carbides MC_y (M = Ti, Zr, Hf, Nb, Ta) and monoxides MO_y (M = Ti, Nb) are systematized for the first time. The effect of nonstoichiometry on the elastic anisotropy of carbides and monoxides is considered. It is shown that the maxima and minima of the spatial three-dimensional distributions of elastic moduli of the discussed nonstoichiometric cubic compou±1 ±1], respectively. It is shown that among the considered nonstoichiometric compounds, cubic titanium monoxide TiO_y has the largest anisotropy of elastic properties, which is a plastic material in terms of the ratio of shear and bulk moduli. An empirical relationship between the elastic stiffness constants c_ij of nonstoichiometric cubic carbides MC_y and their melting temperature is proposed.