An instrumental neutron activation analysis method, using both reactor flux and epi-cadmium neutrons, has been developed for the determination of major, minor and trace elements in sub-seabed sediments. The method involves two different irradiations followed by three different counting periods using high-resolution Ge(Li) and low-energy photon detectors. The list of elements determined includes Ag, Al, As, Ba, Br, Ca, Ce, Cl, Co, Cr, Cs, Dy, Eu, Fe, Ga, Gd, Hf, Hg, I, In, K, La, Lu, Mg, Mn, Mo, Na, Nd, Ni, Pt, Rb, Re, Rh, Sb, Sc, Se, Si, Sm, Sn, Sr, Ta, Tb, Th, Ti, Tm, U, V. W, Yb, Zn, and Zr. The accuracy of the method has been evaluated by analyzing four different standard reference materials. The method has been applied to core samples collected from the Great Meteor East and the South Nares Abyssal Plain which are being evaluated as potential sites for the possible disposal of vitrified highly active waste.