  Using classical differential geometry, the problem of elastic curves and
surfaces in the presence of long-range interactions $\Phi$, is posed. Starting
from a variational principle, the balance of elastic forces and the
corresponding projections ${\bf n}_i\cdot \nabla\Phi$, are found. In the case
of elastic surfaces, a force coupling the mean curvature with the external
potential, $K\Phi$, appears; it is also present in the shape equation along the
normal principal in the case of curves. The potential $\Phi$ contributes to the
effective tension of curves and surfaces and also to the orbital torque. The
confinement of a curve on a surface is also addressed, in such a case, the
potential contributes to the normal force through the terms $-\kappa\Phi -{\bf
n}\cdot \nabla\Phi$. In general, the equation of motion becomes
integro-differential that must be numerically solved.
