We study the relation between intermediate energy nucleon-nucleon scattering and the eigenstates of the bag model using theP-matrix formalism. Data of existing phase-shift analyses are employed to calculate theP-matrix for the coupled1D2(pp) and5S2(NΔ) channels in the energy region above the Δ-isobar production threshold. TheP-matrix calculated for the equivalent hadronic bag radiib=1.4−1.5 fm is shown to have a pole in the mass range 2.31–2.34 GeV in agreement with the MIT bag model prediction of theI=1,J P =2+ 6-quark state with the mass 2.34 GeV. The hadronic shift of this state is shown to be ≈200 MeV; the dibaryon pole of theS-matrix is located at the energy 2.15–2.17 GeV with the width ≈100–200 MeV.