In this paper we prove two main results about obstruction to graph planarity. One is that, if G is a 3-connected graph with a K 5 -minor andOther is that if G is a 3-connected simple non-planar graph not isomorphic to K 5 and e, f ∈ E (G), then G has a minor H such that e, f ∈ E (H) and, up to isomorphisms, H is one of the four non-isomorphic simple graphs obtained from K 3,3 by the addiction of 0, 1 or 2 edges. We generalize this second result to the class of the regular matroids.