Novel classes of tough composites inspired by natural biological materials like nacre, which possesses a multiscale structure with a lamellar microarchitecture, have attracted significant attention for use in structural and energy-related applications. The current theoretical understanding of the toughening and deformation mechanisms of nacre, which could serve as guidelines for composite development, is based on limited material parameters. Here, we report an experimental and numerical study on the transverse isotropic elastic constants of nacre and its constituent inorganic tablets based on genetic-algorithm-assisted resonant ultrasound spectroscopy. The results show that, among the five elastic constants measured, the out-of-plane and in-plane Young’s moduli of nacre sampled from Pinctada martensii were 72.3 and 74.8 GPa, respectively. The remaining out-of-plane and in-plane Poisson’s ratios and out-of-plane shear modulus were 0.23, 0.24, and 21.3 GPa, respectively. Similar trends were observed for the constituent tablets, however, the Young’s moduli were slightly higher at 72.7 and 75.0 GPa, respectively. These results concerning the transverse isotropic elastic properties of nacre and its constituent tablets aid in realizing the bio-duplication of novel nacreous composite materials.