Let f be a univariate monic integral polynomial of degree n and let (↵1, . . . , ↵n) be an n-tuple of its roots in an algebraic closureQ of Q. Obtaining an algebraic representation of the splitting field Q(↵1, . . . , ↵n) of f is a question of first importance in e↵ective Galois theory. For instance, it allows us to manipulate symbolically the roots of f . In this paper, we propose a new method based on multi-modular strategy. Actually, we provide algorithms for this task which return a triangular set encoding the splitting ideal of f . We examine the ability/practicality of the method by experiments on a real computer and study its complexity.