For the homogenization of fiber composites, the equivalent inclusion method is proposed as an alternative to costly full-field methods and less accurate mean-field or effective-field approaches. We take advantage of the slenderness of the inhomogeneities to overcome the “curse of dimensionality” that was evidenced previously for this method. The resulting method is shown on a number of examples to be both accurate and computationally efficient. It is also extremely versatile, as it applies to a large variety of physical problems (beyond electric conductivity considered here).