The coupled-cluster method (CCM) is applied to the spin-1/2 XXZ model for the 1D chain and the 2D square lattice in the region -1 <Δ <1. A CCM model state is chosen in which all spins lie in the xy plane with nearest-neighbour spins anti-parallel. Very good agreement with the exactly known ground-state energies in 1D is obtained, and good agreement with Monte Carlo results is obtained for the 2D case. The sublattice magnetization is obtained, and evidence of phase transition points in both 1D and 2D is presented. The critical behaviour of the 1D ground-state energy near the ferromagnetic phase transition point is investigated.