Interfacial pressure jump terms based on the physics of phasic interface and bubble dynamics are introduced into the momentum equations of the two-fluid model for the bubbly flow. The pressure discontinuity across the phasic interface due to the surface tension for ce is expressed as a function of the fluid bulk moduli and the babble radius. The consequence is that rye obtain from the system of equations the real eigenvalues representing the void-fraction propagation speed and pressure wave speed in terms of the bubble diameter. Inversely, we can obtain an analytic closure relation for the radius of bubbles in the bubbly flow by using the kinematic wave speed given empirically in the literature. It is remarkable to see that the present mechanistic model can indeed represent both the babble dynamics and the two-phase wave propagation in bubbly flow. Finally, it has been shown that the numerical stability is improved significantly if the interfacial pressure jump ter ms are used in lien of the virtual mass terms.