Time resolved pump and probe acoustics and first-principles calculations were employed to assess elastic properties of the TbMnO3 perovskite manganite having orthorhombic symmetry. Measuring sound velocities of bulk longitudinal and shear acoustic waves propagating along at least two different directions in the high symmetry planes (100), (010) and (001), provided a powerful mean to selectively determine the six diagonal elastic constants C11= 227 GPa, C22= 349 GPa, C33= 274 GPa, C44= 71 GPa, C55= 57 GPa, C66= 62 GPa. Among the three remaining off-diagonal ones, C23= 103 GPa was determined with a bissectrice direction. Density functional theory calculations with colinear spin-polarized provided complementary insights on their optical, elastic and magnetoelastic properties.