A spin system with truncated secular dipolar coupling is studied by Monte Carlo calculations. The spins are arrayed on a simple-cubic lattice with periodic boundary conditions. The spin system is investigated in three cases corresponding to the magnetic field, B→0, along the [111] direction at positive spin temperature T and to B→0 along the directions [110] and [111] at negative T. The ordered spin structures have in all three cases a periodicity of four layers at low values of |T|. The Monte Carlo calculations show in two of the cases that the low-|T| structure is the only ordered phase, and that the transition to the paramagnetic phase is of first order. In the remaining case the Monte Carlo calculations suggest a first-order transition to a sinusoidal phase with a periodicity of five layers. A mean-field calculation indicates that the spin system may actually possess a larger number of stable phases than observed in the Monte Carlo calculations. This is discussed in terms of possible periodic structures in the finite lattice. The results are compared with the results of NMR experiments on the ordered nuclear spin system in CaF2.