The elastic properties of crystals are fundamental for structural material. However, in the absence of macroscopic single crystals, the experimental determination of the elastic tensor is challenging because the measurement depends on the transmission of stress inside the material. To avoid arbitrary hypotheses about stress transfer, we combine hydrostatic pressure and uniaxial-stretching experiments to investigate the elastic properties of cellulose Iβ. Three orthogonal compressibilities are 50.0, 6.6, and 1.71 TPa-1. Combining Poisson's ratios from a uniaxial stretching experiment directly gives the Young's modulus along the chain direction (E33). However, Poisson's ratio depends on the deformation rate leading to apparent modulus E33 = 113 GPa using a slow cycle (hours) and 161 GPa using a fast cycle (minutes). The lattice deformation along the chain is not time-dependent, so the off-diagonal elements are time-dependent on the scale of minutes to hours.