The effect of pressure on the elastic constants of high temperature superconductor La 1.8 Sr 0.2 CuO 4 (LSCO) has been studied theoretically using finite strain elasticity theory. The pressure derivatives of the second-order elastic constants of La 1.8 Sr 0.2 CuO 4 are calculated from the knowledge of its second-and third-order elastic constants. The strain energy density / is estimated by taking into account the interactions of nine nearest neighbors of each atom in the unit cell of La 1.8 Sr 0.2 CuO 4 . The energy density / thus obtained is compared with the strain-dependent lattice energy derived from continuum model approximation. The expressions for the effective second-order elastic constants of LSCO system have been derived in its strained state in terms of the natural state second-and third-order elastic constants. These expressions are employed to obtain the pressure derivatives of the effective second-order elastic constants. The results that the larger pressure derivative (dC 33 /dp) along c-axis direction than that along ab-plane, i.e. (dC 11 /dp), corroborates the observation that the layers close-up substantially under hydrostatic pressure while change in interatomic distance in a layer is smaller in La 1.8 Sr 0.2 CuO 4 .