The fcc(gamma) --> hcp(epsilon) martensitic transformation in Fe-Mn-Si based shape memory alloys proceeds through a stacking fault mechanism. In the present paper, the symmetry characteristics of stacking faults are described by using the layer group theory, indicating that the intrinsic SF belongs to P-(6) over bar 2m and the extrinsic fault to P-321 The fault tetrahedron exhibits some sort of symmetry too. According to various repeating structures of the close-packed planes, transition states of the formed martensite are listed and exemplified. A thermodynamic method is proposed to calculate their chemical free energies and evaluate their stabilities which are in the order of 2H > 4H > 5H > 6H > 8H.