In order to obtain more reliable values of diamond's third-order elastic constants, experiments on bulk acoustic wave propagation under uniaxial stress application (up to 450 MPa) in pure IIa-type synthetic single-crystal diamond were carried out, and values of third-order elastic constants were calculated. We have also provided theoretical analysis using ab initio density functional theory approach which has shown close correspondence with the experimentally measured data. From ab initio calculations, the values of third-order elastic constants are (GPa): C (111) = -7611, C (112) = -1637, C (144) = -199, C (155) = -2799, C (123) = 604, C (456) = -1148, while experimental values are C (111) = -7750 +/- 750, C (112) = -2220 +/- 500, C (144) = -1780 +/- 440, C (155) = -2800 +/- 220, C (123) = 2100 +/- 200, C (456) = -30 +/- 150. The estimated values on diamond's fourth-order elastic constants were obtained. The calculated stress-strain curves for different crystal orientations were investigated, including shear stress for [111] direction. From calculations for [100], [110], and [111] directions, the values of critical stress in case of the pure shear were estimated as 222, 113, and 84 GPa, respectively.