The carbon-13 nuclear magnetic resonance shielding surfaces for the isotropic and anisotropic shielding components, sigma(11), sigma(22), and sigma(33), for C-alpha in N-formylglycine amide, and C-alpha and C-beta in N-formylalanine amide, N-formylvaline amide (chi(1) = 180 degrees, -60 degrees, 60 degrees), N-formylisoleucine amide (all chi(1) = -60 degrees conformers), N-formyl serine amide (chi(1) = 74.3 degrees), and N-formylthreonine amide (chi(1) = 180 degrees, -60 degrees, 60 degrees) have been computed at the Hartree-Fock level by using large, locally dense basis sets. The results for C-alpha in glycine and alanine show the expected similar to 4-5 ppm increase in isotropic shielding of sheet over helical geometries, and the overall breadths of the shielding tensors are very similar for both helical and sheet fragments (\sigma(33) - sigma(11)\ similar to 31-37 ppm). However, for each of the C-beta substituted amino acids (valine, isoleucine, serine, and threonine) our results for C-alpha indicate not only the expected similar to 4-5 ppm increase in shielding of sheet fragments over helical ones but also a large increase in the overall tensor breadths for sheet residues over helical ones, and a change in tensor orientation. On average; the sheet residues have \sigma(33) - sigma(11)\ similar to 34 ppm, while on average the helical value is only similar to 22 ppm. For each C-beta substituted amino acid, the results for C-alpha also show that \sigma(22) - sigma(11)\(sheet) >> \sigma(22) -sigma(11)\(helix). For C-beta, the helical and sheet tensor breadths are in general much more similar for a given amino acid, although the actual magnitudes vary widely from one amino acid to another. Since the individual C-alpha tensor elements, sigma(11), sigma(22), and sigma(33), are all quite sensitive to not only the backbone torsion angles, phi, psi, but also to the side chain torsion angle, chi(1), as well, these results suggest that it will in many instances be possible to deduce both backbone (phi,psi) and side chain (chi(1)) torsion angles from an experimental determination of the three principal elements of the C-13(alpha) shielding tensor, results which can be confirmed in some cases with data on C-beta (and C-gamma). Such an approach, based on quantum chemical calculations, should be useful in determining the structures of both crystalline, noncrystalline, and potentially even soluble peptides and proteins, as well as in refining their structures, using shielding tensor elements.