Let V, W be algebraic subsets of $k^n$, $k^m$ respectively, with n ≤ m. It is known that any finite polynomial mapping f: V → W can be extended to a finite polynomial mapping $F:k^n\to k^m.$ The main goal of this paper is to estimate from above the geometric degree of a finite extension $F:k^n\to k^n$ of a dominating mapping f: V → W, where V and W are smooth algebraic sets.