  The aim of this paper is to extend the Morse theory for geodesics to the
conical manifolds. We define these manifolds as submanifolds of $\R^n$ with a
finite number of conical singularities. To formulate a good Morse theory we
must use an appropriate definition of geodesic. The main theorem of this paper
claims that, although the energy is nonsmooth, we can find a continuous
retraction of its sublevels in absence of critical points. So, we can give a
good definition of index for isolated critical values and for isolated critical
points. We prove that Morse relations hold and, at last, we give a definition
of multiplicity of geodesics which is geometrical meaningful.
