Under the assumption that most of elastic scatterings at very high energies are the unitary reflection—such as the shadow scattering—of inelastic collisions resulting in the classical heavy boson wave excitation, some important interrelations between the elastic scattering and the multiple particle production at very high energies are investigated. Recent analyses of cosmic ray jets have suggested that direct products of the multiple particle production are mainly heavy bosons rather than pions, and that observed pions come from the decay of heavy bosons. Two extreme cases are considered of the final states of the boson assembly; (i) no correlation case, and (ii) coherent boson wave case. The real ststes would be between the two cases. The boson assembly with no correlations are well described by a classical boson wave state which may be identified with the eigenstate of the boson annhilation operator. The coherent wave state, describing the definite phase wave, is defined by the eigenvector of the phase operator. One of the important results is such that there hold the relations between the mean variance δN and the average N̅ of the boson multiplicity, and that the mean variance of the boson momentum δk or of the invariant momentum transfer δΔ must depend on the primary energy p like where β = 1 in the no correlation case and β≪ 1 in the coherent wave case. The present status of experiments is too poor to descriminate sharply between both cases, although the above results are consistent with experiments. Qualified high energy data above about 1,000 GeV are highly desired. In the no correlation case the interrelations between the elastic diffraction scattering and the multiple particle production are formulated in some details, and it is shown that the results are consistent with the existing experiments. Some brief remarks are given on the large angle elastic scattering and the anti-shrinkage of the proton-antiproton diffraction peak. Finally a fundamental assumption on the asymptotic behavior of the elastic scaattering amplitude in the modern S matrix theory is criticized from the viewpoint of the multiple particle production phenomena. In Appendices some mathematical supplements are given for the eigenvectors of the boson annihilation operator and their reciprocal vectors, and the physical meaning of the complex energy variable and the analytic continuation of the elastic scatteing amplitude are discussed.