This text proposes a new method for fuzzy rule extraction from support vector machines (SVMs) trained to solve classification problems. SVMs are learning systems based on statistical learning theory and present good ability of generalization in real data base sets. These systems have been successfully applied to a wide variety of application. However SVMs, as well as neural networks, generates a black box model, i.e., a model which does not explain the process used in order to obtain its result. Some considered methods to reduce this limitation already has been proposed for the binary classification case, although they are restricted to symbolic rules extraction, and they have, in their antecedents, functions or intervals. However, the interpretability of the symbolic generated rules is small. Hence, to increase the linguistic interpretability of the generating rules, we propose a new technique for extracting fuzzy rules of a trained SVM. Moreover, the proposed model was developed for classification in multiple classes, which was not introduced till now. Fuzzy rules obtained are presented in the format if x1 belongs to the fuzzy set C1, x2 belongs to the fuzzy set C2 , … , xn belongs to the fuzzy set Cn , then the point x=(x1, x2, …xn) belongs to class A. For testing this new model, we performed detailed researches on four data bases: Iris, Wine, Bupa Liver Disorders and Wisconsin Breast Cancer. The rules´ coverage resultant of the application of this method was quite good, reaching 100% in Iris case. After the rules generation, its evaluation was performed using two criteria: coverage and accuracy. Besides the testing above, the performance of the methods for multi-class SVM described in this work was evaluated.