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This note deals with some effective results in Mahler's method. In a recentwork, we used a theorem of Philippon to show that given a Mahler function$f(z)$ in ${\bf k}\{z\}$, where ${\bf k}$ denotes a number field, and analgebraic number $\alpha$ in the domain of holomorphy of $f$, the number$f(\alpha)$ is either transcendental or belongs to ${\bf k}(\alpha)$. Wedescribe here an effective procedure to decide if such a number istranscendental or not. More generally, given several Mahler functions$f_1(z),\cdots,f_r(z)$ and an algebraic number $\alpha$ in the domain ofholomorphy of these functions, we show how to effectively determine a basis ofthe vector space of $\overline{\mathbb Q}$-linear relations between$f_1(\alpha),\cdots,f_r(\alpha)$.

M\'ethode de Mahler, transcendance et relations lin\'eaires : aspects effectifs