  We perform atomic relativistic many-body calculations of the field isotope
shifts and calculations of corresponding nuclear parameters for all stable
even-even isotopes of Yb$^+$ ion. We demonstrate that if we take nuclear
parameters of the Yb isotopes from a range of the state-the-art nuclear models
which all predict strong quadrupole nuclear deformation, then calculated
non-linearity of the King plot, caused by the difference in the deformation in
different isotopes, is consistent with the non-linearity observed in the
experiment (Ian Counts {\em et al}, Phys. Rev. Lett. {\bf 125}, 123002 (2020)).
The changes of nuclear RMS radius between isotopes extracted from experiment
are consistent with those obtained in the nuclear calculations.
