  In this paper we classify the homotopy classes of proper maps $E\rightarrow
\mathbb R^k$, where $E$ is a vector bundle over a compact Hausdorff space. As a
corollary we compute the homotopy classes of proper maps $\mathbb
R^n\rightarrow \mathbb R^k$. We find a stability range of such maps. We
conclude with some remarks on framed submanifolds of non-compact manifolds, the
relationship with proper homotopy classes of maps and the Pontryagin-Thom
construction.
