A relativistic formulation of the SU(6) symmetry scheme is presented, starting with the basic assumption that the fields corresponding to elementary particles are tensors of M(12) [or U~(12) or SU(12)L]. In particular a mixed second-rank tensor and a totally symmetric third-rank tensor are associated with the meson and baryon fields, respectively. It is shown that if these fields are required to satisfy prescribed free-field equations of motion, then one is led to a particle supermultiplet structure which corresponds to the 35⊕1 and 56-dimensional representations of SU(6) for the mesons and baryons. It is also shown that the spin-dependent and SU(3)-spin-dependent mass splittings can be included in the theory and that solutions in terms of physical particle fields can be obtained. Effective trilinear meson-meson and meson-baryon vertex functions, using these solutions and an interaction Lagrangian which is invariant under M(12), are calculated in the lowest order perturbation. We would like to note especially the following results: (a) From the known pion-nucleon coupling constant, the width of the pion-nucleon (3,3) resonance is calculated to be 94 MeV. (b) The ratio of the magnetic form factors for the neutron and proton is - 2/3 for all momentum transfers and μP=(1+2MPmρ) nuclear magnetons. (c) The charge form factor of the neutron is zero for all momentum transfers.