A method for calculating the chemical shielding tensor of any atom with the QM/MM approach has been developed. The method is described and applied to a number of model systems including the water dimer, NMA-water complexes, cytosine monophosphate, paired and stacked nucleic acid bases, imidazole-metal complexes, and 1'-deoxyribose-metal ion complexes. The results demonstrate that with an appropriate QM/MM partition, good descriptions of the environmental effects on chemical shift tensors are obtained. The typical error compared to full QM calculations is 1-2 ppm for heavy atoms. At distances below 2.5 Angstrom, such as occur in hydrogen bonding, larger errors arise due to the lack of Pauli repulsion and magnetic susceptibility of the nearby groups in the current QM/MM model; including the hydrogen bonded molecules as part of the QM region is a way of solving this problem. The method is also applied to a simple model of myoglobin-CO and it is shown that the significant influence from the distal histidine on the shielding of Fe and CO is well reproduced by a QM/MM calculation. Application to the chemical shift of the 1-N nitrogen in nicotinamide adenine dinucleotide (NAD(+)), relative to N-methyl nicotinamide, gives good results, indicating that accurate chemical shifts can be obtained for specific atoms in large molecules that cannot be treated by QM at the MP2 level. The effect of solvation on the chemical shift of water was also studied with the QM/MM approach in a molecular dynamics framework. The test calculations described in this paper demonstrate that the QM/MM method for estimating shielding tensors and chemical shifts is a useful approach for large systems.