The C-13 and N-15 chemical shifts of the alpha and gamma crystal forms of nylon 6 have been estimated using ab initio calculations (GIAO method) with the B3LYP Density Functional and the 6-311G(d) basis set. Calculations were applied on proper model systems and the agreement with experimental data was quite good in all cases. Comparison between the results obtained for isolated chains and hydrogen bonded sheets allowed to elucidate the influence of the conformation and packing forces in the chemical shifts. These results open up new opportunities for the future use of quantum mechanical calculations as a complementary tool in the determination of the crystal structure of polymers.