AbstractWe consider massive classical matter fields with spin 1/2, 1, 3/2 and 2 in the flat Minkowski spacetime. By the method of Gordon, we decompose their respective momentum and spin current densities into their convective and polarisation parts (see eqns. (10a, b)). We find the translational and rotational gravitational moment densities of these fields. Their general properties are discussed and we draw some conclusions for a gauge theoretical treatment of gravity.