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A realistic theoretical study to predict the phonon dispersion and binding energy of h.c.p. metals is developed. The total interaction among the constituents is divided into two parts, ion-ion part and electron-ion-electron part. The former part is expressed by the modified form of the generalized exponential potential (MGEP) developed by the present group. To highlight the characteristic features of the MGEP other similar potentials are compared. The latter part is represented by the modified Krebs scheme, involving the dielectric screening due to Vashista and Singhwi. These interactions are blended to develop a model for predicting the binding energy and the phonon dispersion of the scantily studied h.c.p. metals like thallium.