Our purpose in this paper is to understand the geometry of the Poincaré compactifcation and to apply this technique to prove that there exists a Poincaré compactifcation of vector felds defned by rational functions and of vector feld that are the quotient of some power of polynomial. We will give also a global expressions for the Poincaré vector feld associated. Furthermore, we summarize these results proving that there exist a Poincaré vector feld for any vector feld whose rate of growth at infnity of each component is not bigger than a polynomial growth.