In spite of elementarity of this question, there was no significant progress in order to answer it. Also, it is known that Whitehead Conjecture is equivalent to some purely-algebraic problem on finitely generated free groups. Here we suggest a new, geometrical, point of view on the Whitehead Conjecture, which, may be, will be more productive. Let us introduce some notation. Let P and Q be polyhedra.
P is called collapsible if the preimages of points under f are collapsible polyhedra.
P with Q a special polyhedron. Using the slight modification of this result and the fact that a collapsible map is a homotopy equivalence on its image, we prove the following Theorem. B.G. Casler, An imbedding theorem for connected 3-manifolds with boundary , Proc.