The Monte Carlo technique is used to calculate the static properties of spin systems with an interaction described by a secular dipolar Hamiltonian with a finite range of interaction. The spins are arranged in a simple cubic lattice with periodic boundary conditions. The static spin structures are determined for the magnetic field along the three directions [001], [110], and [111], both at positive and at negative spin temperatures. The spin structures, which are of antiferromagnetic type, are compared to predictions based on the mean-field theory and to NMR experiments on CaF2. Two of the antiferromagnetic spin systems are investigated in detail and the following properties are calculated: the critical temperature, spontaneous sublattice magnetization, internal energy, heat capacity, bulk and staggered susceptibilities, and pair- and autocorrelation functions. Series expansions of a number of properties in the paramagnetic phase support the results of the Monte Carlo calculations. The Monte Carlo data are used to derive the critical exponents and critical amplitudes for the spontaneous sublattice magnetization, longitudinal staggered susceptibility, and inverse correlation length. The critical parameters for the two antiferromagnets are discussed within the concepts of the static scaling and universality hypotheses. The parameters are consistent with the classification of the antiferromagnets within the universality class of the three-dimensional Ising model.