The neutral matter distribution inside proton and deuteron is deduced from the ela,;tic pp and dd differential cross sections at v s =53 GeV. A model is proposed, which predicts correctly the elastic pd differential cross section quantitatively for the diffraction peak and qualitatively in the large t region. A new criterion is given to distinguish models \\·hich contain a distribution function. Our model leads to the result that the space integral of the deuteron matter distribution function is twice that of proton, as is expected from their masses. It is pointed out that the original Chou-Yang model does not have this feature. Recently very precise measurements have been performedn for the differential cross sections in the elastic pp, pd and dd scatterings at CERN-ISR energies in the large t region. In this paper we deduce a neutral matter distribution of proton from the pp scattering data and that of deuteron from the dd scattering data. On the basis of the distribution functions of the proton and deuteron lYe predict the differential cross section of the elastic pd scattering and compare it with the experimental data. We get quantitatively a very good prediction for the diffraction peak in pd scattering and see qualitatively a good feature in the large t region. There have been many studies to deduce the internal structure of the nucleon. First the electron scattering from the proton gives the charge Se condly the large Pr phenomena of the inelastic scatterings give the information for the internal structure of hadron. 3J Thirdly the deep inelastic scatterings supply several results 1> for the quark-parton distribution in the limited momentum space. On the other hand, the pp elastic scattering has been analyzed by the Chou-Yang model6J and so on. By means of one variation of the Chou-Yang model it is suggested 7J that the number of quarks is three inside the proton. But as far as the author knows, it seems that there are few works 8J for the deduction of the matter distribution inside the proton from the viewpoint of the elastic hadron-hadron differential cross section. Since the equality Utot (PP) =Gtot (np) is experimentally confirmed 9J for ys>5 Ge V, we interpret that the obtained matter distribution is not charged but neutral, which is called a gl uon distribution. Since the Chou-Yang model 6> is constructed based on the matter distribution function, this model can give us the matter distribution of proton from PP scatter ing data. In the Appendix the explicit method is given to deduce the distribution.