Abstract.This paper is devoted to showing how to compute the Puiseux expansions of a polynomial in $\mathbb{L}[x,y]$ with $\mathbb{L}$ an algebraically closed field of characteristic 0 by using a matricial version of Hensel's Lemma over the companion matrix of the considered polynomial together with Dynamic Evaluation to deal with the involved algebraic numbers. First experimental results show a better behaviour than the classical methods based upon the Newton polygon.