  Given interpolation points $P_1,P_2,\ldots,P_n$ in the plane, it is known
that there does not exist an interpolating curve with minimal bending energy,
unless the given points lie sequentially along a line. We say than an
interpolating curve is {\it admissable} if each piece, connecting two
consecutive points $P_i$ and $P_{i+1}$, is an s-curve, where an {\it s-curve}
is a planar curve which first turns at most $180^\circ$ in one direction and
then turns at most $180^\circ$ in the opposite direction. Our main result is
that among all admissable interpolating curves there exists a curve with
minimal bending energy. We also prove, in a very constructive manner, the
existence of an s-curve, with minimal bending energy, which connects two given
unit tangent vectors.
