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This work presents the results of experimental and theoretical studies of the magnetic properties of the LiYb F 4 single crystal and powder samples, and magnetoelastic properties of the LiYb F 4 single crystal samples, at low temperature and applied field range of 0-9 T. The magnetostriction experimental data for the single crystal of LiYb F 4 is published for the first time. The magnetization and magnetostriction were calculated in the framework of the exchange-charge model taking into account dipole–dipole and electron-deformation interactions, with the calculation of the electron-deformation parameters. The theoretical analysis presents quantitative agreement in the temperature range of 2–10 K with the magnetization and magnetostriction measurements of the LiYb F 4 samples. • Experimental magnetostriction data shows high anisotropy of the magnetoelastic properties. • Exchange-charge model describes magnetic properties of LiYb F 4 crystals at 2 < T < 300 K. • Magnetic properties of LiYb F 4 single crystal have four-fold symmetry. • Set of electron-deformation parameters for LiYb F 4 was calculated. [ABSTRACT FROM AUTHOR]