We show how to compute the pre-images of multiplication by 3 in the group of points of an elliptic curve E over a field k of characteristic different from 2 and 3 such that E [3](k)= E [3]. We show Q=(x Q, y Q)∈[3] E (k) if and only if y Q− d− m (x Q− c) is a cube in k for every 3-torsion point (c, d)∈ E [3], where m is the slope of the tangent to E at (c, d). We reduce our problem to the computation of at most 2 independent cubic roots plus a few polynomial operations.