An attempt is made to study the carrier contribution to the elastic constants under magnetic quantization in III-V, II-VI, PbTe/ PbSnTe, strained layer and HgTe/CdTe superlattices (SLs) with graded interfaces and compare the same with that of the constituent materials by formulating the respective dispersion laws. It is found, taking GaAs/ Ga1-xAlxAs, CdS/CdTe, PbTe/ PbSnTe, InAs/GaSb and HgTe/CdTe with graded interfaces as examples, that the second and third order elastic constants exhibit oscillatory dependence with the inverse quantizing magnetic field due to the Shubnikov-de-Haas (SdH) and allied SL effects and increases with increasing electron concentration in an oscillatory manner in all the cases. The nature of oscillation is totally band structure dependent and the width of the finite interface enhances the numerical values of the second and third order elastic constants for all the aforementioned SLs. The numerical values of the second and third order elastic constants in graded superlattices are greater than that of the constituent materials. We have suggested an experimental method of determining the electronic contribution to the elastic constants in materials having arbitrary dispersion laws and the theoretical results are in quantitative agreement with the suggested relationship. In addition, the well-known expressions for the bulk specimens of wide gap materials have also been obtained as special cases of our generalized analysis under certain limiting conditions. © 2004 Elsevier B.V. All rights reserved.