The differential cross-section for the elastic scattering of heavy ions like C and Si scattered from the target nuclei C, Pb, Zr, Ca, O, Si, S, Al at different projectile energies has been studied in terms of the Strong Absorption Model of Frahn and Venter using the three parameters version of this model. We find that a reasonably good description to the angular distribution of the experimental elastic scattering data is possible. The parameters of the model are cut-off angular momentum T, the rounding parameter ?, and the real nuclear phase-shift ?. The quality of fit to the experiment is nearly of similar nature to that achieved by optical model. The optical model has nine to twelve adjustable parameters where as the model SAM has only three. The three parameters of SAM model are quite sufficient to analyze the experimental elastic scattering data. From such an analysis, the extracted SAM parameters are unique whereas the optical model parameters suffer from discrete and continuous ambiguities and that is why the parameters of the optical are not unique.