The nuclear shielding of the Xe atom is a tensor molecular electronic property that is a very sensitive indicator of the local environment. Xe atoms in nanochannels of a crystal exhibit anisotropic NMR line shapes that are characteristic of the average shielding tensor; the line shape is a manifestation of the systematic variation of the observed component of the tensor with the orientation of the nanochannel axis in the static uniform external magnetic field. In this paper, a method of calculating the Xe line shapes in nanochannels is presented. The averaging of the shielding tensor is carried out with a grand canonical ensemble at constant (mu, V, T). The line shapes are obtained by assuming a random distribution of orientations of the crystallites within a sample. The equivalent procedure is carried out by finding the component of the Xe shielding tensor along the magnetic field directions selected uniformly on the surface of a sphere. The approach developed here is used to predict the general behavior of Xe line shapes for Xe in elliptical channels of nanoscale dimensions. The channel architecture of crystalline aluminum phosphate ALPO-11 with dimensions 6.7x4.4 Angstrom is used here as a model channel architecture. ALPO-11 is known to impose on Xe atoms an intermolecular NMR shielding response that is highly deshielded compared to a free Xe atom and with a line shape systematically changing with Xe occupancy [J. A. Ripmeester and C. I. Ratcliffe, J. Phys. Chem. 99, 619 (1995)]. In the present work, model channels are constructed with Ne or Ar atoms in the ALPO-11 architecture, and grand canonical Monte Carlo simulations of Xe in these model channels are carried out. The difficulty lies in the construction of the Xe chemical shift tensor for each Xe in the channel at each configuration. We propose a new approach to calculations of the Xe chemical shift tensor in a nanochannel: the additive dimer tensor model. For a model nanochannel constituted entirely of rare gas atoms (Ne, for example) that are located at the crystallographic positions of the atoms constituting the channel walls, the Xe shielding tensor is determined as follows: For a given configuration of Xe atoms within the channel, the Xe shielding tensor of the Jth Xe atom at position (x(J),y(J),z(J)) is calculated by a summation over all i of the contribution of Xe-J-Ne-i dimer, the Ne atom located at the ith position, using the ab initio Xe-Ne rare gas dimer shielding tensor. To this is added the Xe-Xe contributions that are calculated by a summation over all L of the contribution of the Xe-J-Xe-L dimer, using the ab initio Xe-Xe dimer shielding tensor. The systematic variations with Xe occupancy of the line shapes obtained from GCMC simulations using the additive dimer tensor model in the model Ne and Ar channels are used to provide general insight into the average Xe shielding tensor in nanochannels. The invariant qualitative aspects of the behavior of Xe line shapes in the model channels provide general predictions independent of the atoms constituting the channel. The chemical shift response of the Xe to the specific atoms constituting the channel walls provides the quantitative details. The specific application to Xe in ALPO-11 crystals compares favorably with experiment.