  We present the mechanics of a model of supersolid in the frame of the
Gross-Pitaevskii equation at $T=0K$ that do not require defects nor vacancies.
A set of coupled nonlinear partial differential equations plus boundary
conditions is derived. The mechanical equilibrium is studied under external
constrains as steady rotation or external stress. Our model displays a
paradoxical behavior: the existence of a non classical rotational inertia
fraction in the limit of small rotation speed and no superflow under small (but
finite) stress nor external force. The only matter flow for finite stress is
due to plasticity.
