We present theoretical study of the pressure coefficient of the light emission (dE E / dP ) in compressively strained zinc-blende InGaAs/GaAs and InGaN/GaN quantum wells, grown in a (001) direction. We investigate the contributions to dE E / dP arising from (i) third-order (nonlinear) elasticity, (ii) nonlinear elasticity, originating from pressure dependence of elastic constants, and (iii) nonlinear dependence of elastic constants on composition in InGaAs and InGaN alloys. The obtained results indicate that the use of nonlinear elasticity is essential for determination of dE E / dP in the strained InGaAs/GaAs and InGaN/GaN quantum wells, while the inclusion of the nonlinear dependence of elastic constants on composition of InGaAs and InGaN alloys does not improve agreement between the theoretical end experimental values of dE E / dP in the considered structures.