  Fourth-rank tensors of complete Voigt's symmetry, that embody the elastic
properties of crystalline anisotropic substances, were constructed for all 2D
crystal systems. Using them we obtained explicit expressions for inverse of
Young's modulus E, inverse of shear modulus G and Poisson's ratio, which depend
on components of the elastic compliances tensor S, on direction cosines of
vectors n of uniaxial load and the vector m of lateral strain with crystalline
symmetry axes. All 2D crystal systems are considered. Such representation
yields decomposition of the above elastic characteristics to isotropic and
anisotropic parts. Expressions for Poisson's coefficient are well suited for
studying the property of auxeticity and anisotropy 2D crystals. Phase
velocities are calculated for all 2D crystal classes.
