Theoretically calculated binding energies of H3 and He3 were reported in our preceding paper, I, where two-body forces of exponential type with hard core cut-offs were assumed. In the present paper we show the results of similar calculations with two-body forces of the Yukawa type which are cut off by hard cores. Only central forces are used and the force parameters are determined from the two-nucleon data at low energies as was done in the preceding paper. This change in the radial form of the nuclear force does not alter the qualitative features of the effects of hard cores: i. e. 1) Hard cores reduce the binding energies of H3 and He3. 2) Hard cores push out the wave functions of H3 and He3,so that the Coulomb energy of He3, which is too large without the hard cores, is brought into agreement with the experimental value of the difference between the binding energies of H3 and He3.