Elastic characterization of wide direct band gap semiconductor cadmium sulfide has been studied using finite strain elasticity theory. The complete sets of second and third order elastic constants are obtained using the method of homogeneous deformation for single crystal cadmium sulfide in hexagonal wurtzite phase. All the third order elastic constants are negative; indicating an increase of vibrational frequencies under stress, giving rise to an increase in the strain energy. The longitudinal wave velocities C 111, C 222 and C 333 in the single crystal cadmium sulfide is greater than the shear wave velocity. The six first order pressure derivatives of the second order elastic constants obtained indicate the higher compressibility of the cadmium sulfide crystal along the c-axis. The generalised Gruneisen parameters of the acoustic waves and the low temperature limit of lattice thermal expansion are determined. The obtained results are compared with the available reported values.