Let k be a perfect field of characteristic p > 2 and K an extension of F = Frac W ( k ) contained in some F ( μ p r ) . Using crystalline Dieudonné theory, we provide a classification of p-divisible groups over R = O K [ [ t 1 , … , t d ] ] in terms of finite height ( φ , Γ ) -modules over S : = W ( k ) [ [ u , t 1 , … , t d ] ] . When d = 0 , such a classification is a consequence of (a special case of) the theory of Kisin–Ren; in this setting, our construction gives an independent proof of this result, and moreover allows us to recover the Dieudonné crystal of a p-divisible group from the Wach module associated to its Tate module by Berger–Breuil or by Kisin–Ren.