The effect of anisotropies on the energy gap and magnetization for odd number of coupled quantum spin-1/2 antiferromagnetic anisotropic Heisenberg systems is investigated using the linear spin wave theory. However, for the chains, the energy gap opens above a critical anisotropy. While, for the planes, in the isotropic case, such system exhibits a long-range order and no energy gap. Whereas, in the anisotropic case the energy gap opens above a critical anisotropic value. Known results of the isotropic case have been obtained.