  In the framework of the geometrically nonlinear 6-parameter resultant shell
theory we give a characterization of the shells without drilling rotations.
These are shells for which the strain energy function $W$ is invariant under
the superposition of drilling rotations, i.e. $W$ is insensible to the
arbitrary local rotations about the third director $\boldsymbol{d}_3\,$. For
this type of shells we show that the strain energy density $W$ can be
represented as a function of certain combinations of the shell deformation
gradient $\boldsymbol{F}$ and the surface gradient of $\boldsymbol{d}_3\,$,
namely $W\big(\boldsymbol{F}^{ T}\boldsymbol{F} , \,
  \boldsymbol{F}^T \boldsymbol{d}_3 \,, \,
\boldsymbol{F}^T\mathrm{Grad}_s\boldsymbol{d}_3 \big)$. For the case of
isotropic shells we present explicit forms of the strain energy function $W$
having this property.
