β-Eucryptite (LiAlSiO₄) shows anisotropic thermal expansion as well as one-dimensional superionic conductivity. We have performed the lattice dynamical calculations using ab-initio density functional theory along with inelastic neutron scattering measurements. The anisotropic stress dependence of the phonon spectrum is calculated to obtain the thermal expansion behavior along various axes. The calculations show that the Gr€uneisen parameters of the low-energy phonon modes around 10 meV have large negative values and govern the negative thermal expansion behavior at low temperatures along both the “a”- and “c”-axes. On the other hand, anisotropic elasticity along with anisotropic positive values of the Gr€uneisen parameters of the high-energy modes in the range 30–70 meV are responsible for the thermal expansion at high temperatures, which is positive in the a-b plane and negative along the c-axis. The analysis of the polarization vectors of the phonon modes sheds light on the mechanism of the anomalous thermal expansion behavior. The softening of a  Γ-point mode at about 2 GPa may be related to the high-pressure phase transition.