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Angular distributions of the elastic scattering of the system /sup 12/C+/sup 28/Si were measured at the energies E/sub CM/ = 14.70; 16.08; 18.90; 20,97; 21.87 MeV, in the angular range 15/sup 0/ (le) (theta)/sub CM/ (le) 170/sup 0/, with angular steps of 1/sup 0/. Other seven angular distributions measured by Villari, Ost and Cheng at energies E/sub CM/ = 17.50; 19.60; 20.30; 22.40; 23.80; 24.50 and 25.20 MeV, have also been used in our analysis. The angular distributions have been reproduced by optical model calculations and new optical potentials for the system /sup 12/C+/sup 28/Si were obtained. Calculations of the total reaction cross section from the elastic scattering data using a model independent method were done. The results were compared with fusion cross section data and with total reaction cross sections obtained via optical model calculations. Finally experimental angular distributions were analysed by phase shift analysis and the problem of unicity and ambiguities of the scattering matrix S(l) was discussed. (Atomindex citation 20:065147)