  We consider shells in three dimensional Euclidean space which have bounded
principal curvatures. We prove Korn's interpolation (or the so called first and
a half\footnote{The inequality first introduced in [6]}) and second
inequalities on that kind of shells for $\Bu\in W^{1,2}$ vector fields,
imposing no boundary or normalization conditions on $\Bu.$ The constants in the
estimates are optimal in terms of the asymptotics in the shell thickness $h,$
having the scalings $h$ or $O(1).$ The Korn interpolation inequality reduces
the problem of deriving any linear Korn type estimate for shells to simply
proving a Poincar\'e type estimate with the symmetrized gradient on the right
hand side. In particular this applies to linear geometric rigidity estimates
for shells, i.e., Korn's fist inequality without boundary conditions.
