This paper presents a theoretical study of the size evolution of equilibrium structures and approximate HF vibrational red shifts for ArnHF van der Waals clusters, with n = 1-14. Pairwise additive ArnHF intermolecular potential energy surfaces were constructed from spectroscopically accurate Ar-Ar and anisotropic Ar-HF potentials. The latter depend on vibrational excitation of the HF monomer. The global and energetically close-lying local minima of ArnHF, n = 1-14, for HF v = 0 and v = 1, were determined using simulated annealing followed by a direct minimization scheme. For ArnHF clusters with n less than or equal to 8, the lowest-energy structure always has HF bound to the surface of the Ar-n subunit. In contrast, for n greater than or equal to 9, the global minimum of ArnHF corresponds to HF inside a cage. Ar12HF has the minimum-energy configuration of an HF-centered icosahedron, which appears to be unusually stable. Size dependence of the HF vibrational red shift in ArnHF (n = 1-14) clusters was investigated by means of a simple approximation, where the red shift was represented by the energy difference between the global minima of a cluster obtained for HF v = 0 and v = 1, respectively. The approximation reproduced rather accurately the experimentally determined variation of the Ar,HF red shift with the number of Ar atoms, for n = 1-4, although it overestimated their magnitude. For larger Ar,HF clusters, 4 < n less than or equal to 14, a nonmonotonic, step-like dependence of the red shift on the cluster size is predicted, which can be interpreted in terms of changes in the minimum-energy cluster geometries. The predicted red shift for the icosahedral Ar12HF, where the first solvation shell is full, is 44.70 cm(-1), which is only 5.4% higher than the experimental HF vibrational red shift in an Ar matrix, of 42.4 cm(-1).