SUMMARY
An investigation for directions of extreme - maximum or minimum - values of the longitudinal and transverse stiffness moduli as well as of the limit uniaxial and limit shear stresses in anisotropic linear elastic solids is performed in the paper. The cases of cubic symmetry (regular crystal system) and of volumetrically isotropic cylindrical symmetry (hexagonal crystal system with additional constraints) are considered. The systems of non-linear equations for the components of the versors of investigated directions are derived with use of the spectral decomposition of the elasticity (stiffness and compliance) tensors.