  From the topological viewpoint, Morse shellings of finite simplicial
complexes are {\it pinched} handle decompositions and extend the classical
shellings. We prove that every discrete Morse function on a finite simplicial
complex induces Morse shellings on its second barycentric subdivision whose
critical tiles-or pinched handles-are in oneto-one correspondence with the
critical faces of the function, preserving the index. The same holds true,
given any smooth Morse function on a closed manifold, for any piecewise-linear
triangulation on it after sufficiently many barycentric subdivisions.
