In this paper an attempt is made to study the electronic contribution to the elastic constants of strained III-V materials under high magnetic fields on the basis of k.p theory. It is found taking strained Hg1-xCdxTe and In1-xGaxAsyP1-y lattice matched InP as examples that they increase with increasing doping and oscillate with inverse magnetic field respectively. The strain enhances the numerical values of the elastic constants. The theoretical formulation is in quantitative agreement with the suggested experimental method of determining the above contributions for degenerate materials having arbitrary dispersion laws. In addition, the well-known results for strain free wide gap materials in the absence of magnetic field have been obtained from our generalized analysis under certain limiting conditions.