The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Ciência da Computação e Estatística, Instituto de Biociências Letras e Ciências Exatas de São José do Rio Preto, São José do Rio Preto, RUA CRISTOVÃO CRISTOVÃO COLOMBO, 2265 (Sala 15 - DCCE), JD NAZARETH, CEP 15054000, SP, BrasilUniversidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Matemática Aplicada, Instituto de Biociências Letras e Ciências Exatas de São José do Rio Preto