A method for building nite models is proposed. It combines enumeration of the set of interpretations on a nite domain with strategies in order to prune signi cantly the search space. The main new ideas underlying our method are to bene t from symmetries and from the information extracted from the structure of the problem and from failures of model veri cation tests. The algorithms formalizing the approach are given and the standard properties (termination, completeness, and soundness) are proven. The method can deal with rst-order logic with equality. In contrast to existing ones, it does not require to transform the initial problem into a normal form and can be easily extended to other logics. Experimental results and comparisons with related works are reported.