Abstract:The second and third-order elastic constants and pressure derivatives of second-order elastic constants of trigonal LiNbO 3 (lithium niobate) have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivatives of trigonal LiNbO 3 are obtained in the present work. The second and third-order elastic constants are compared with available experimental values. The second-order elastic constant 11 C which corresponds to the elastic stiffness along the basal plane of the crystal is less than 33 C which corresponds to the elastic stiffness tensor component along the c-axis of the crystal. The pressure derivatives, dp C d ij / ′ obtained in the present work, indicate that trigonal LiNbO 3 is compressible. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in LiNbO 3 . The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.