5-th order nonlinear elastic properties of diamond-like single crystals are investigated by computational quantum chemistry, brief introduction to which is supplied. DFT LDA and DFT GGA methods are used to calculate curves of stress dependency on tensile, compressive and shear strains with account of structure relaxation in huge strain range until irreversible deformation occurs at strength limit. Limits of linear elastic proportionality, maximal stresses, regions of necking non-plastic creep are indicated. Relations between linear limits of axial and shear stresses, determined by bilinear approximations of the curves, are represented by Hill's surface as an estimation of plastic anisotropy. Elastic constants are calculated both for finite and small strains. Polynomial approximations are made for dependencies of full energy, crystal volume, Poisson coefficient on strain. Determined parameters can be used for finite-element modelling in mechanical engineering and for reexamination of indentation tests.