  We provide a coordinate-free derivation of the system of equations that
govern equilibrium of a thin shell that can undergo shear. This system involves
tensorial fields representing the internal force and couple per unit length
that disjoint parts of the shell exchange at their common boundary. By an
appropriate decomposition of these tensorial quantities we are able to obtain a
representation of the internal power in terms of time derivative of suitable
strain measures. We use this representation to postulate constitutive
equations. We specialize the theory to case of unshearable shells, and then we
linearize the resulting equations. As an application, we deduce and solve the
equations that govern the free vibrations of a pressurized spherical shell.
