In [16], we characterized the elements of radical of an ideal in MV -algebras. In this paper, we try to give a characterization for elements of radical of an A-ideal in MV -modules. For this purpose, we first present the definition of the envelope of an A-ideal in MV -modules and then verify the relation between the envelope of A-ideals and the radical of A-ideals in MV -modules. Finally, in a variety of circumstances, we offer a formula for identifying the elements of radical of an A-ideal in MV -modules.