The X-ray elastic constants of pressureless sintered β-silicon nitride (Si<sub>3</sub>N<sub>4</sub>), were experimentally determined for ten different diffractions by using Kα radiations of Cu, Co, Fe, Cr and V. The X-ray compliances, (1+<i>v</i>'<sub>x</sub>)/<i>E</i>'<sub>x</sub> and <i>v</i>'<sub>x</sub>/<i>E</i>'<sub>x</sub> (<i>E</i>'<sub><i>x</i></sub>=Young's modulus, <i>v</i>'<sub><i>x</i></sub>=Poisson's ratio), change as a second power function of cos<sup>2</sup>φ (φ=angle between the diffraction plane normal and the <i>c</i>-axis of hexagonal crystal). Using the simplex method, the elastic constants of single crystals of β-silicon nitride were determined from the measured values of the X-ray compliances on the basis of the average of Voigt and Reuss models and Kröner's model, combined with the self-consistent analysis of multi-phase materials. The obtained result shows a high stiffness in the <i>c</i>-direction of hexagonal crystals, but the degree of anisotropy is not so large as the whisker data reported by Hay et al.