Elastic properties at high temperature Superconductors depends on the second order (SOE) and third order (TOE) expressions. The superconductor of La _1.85 Sr_0.15 CuO₄ having tetragonal structure have been derived using the finite deformation theory and variation with Einstein temperature (θ_E), Debye temperature (θ_D) for La _1.85Sr _0.15 CuO₄ at high temperature superconductor. The derived expression have been used to compute the values of SOE and TOE constant of La _1.85 Sr_0.15 CuO₄ material are being presented for the first time.