  We study the Anderson model of localization with anisotropic hopping in three
dimensions for weakly coupled chains and weakly coupled planes. The eigenstates
of the Hamiltonian, as computed by Lanczos diagonalization for systems of sizes
up to $48^3$, show multifractal behavior at the metal-insulator transition even
for strong anisotropy. The critical disorder strength $W_c$ determined from the
system size dependence of the singularity spectra is in a reasonable agreement
with a recent study using transfer matrix methods. But the respective spectrum
at $W_c$ deviates from the ``characteristic spectrum'' determined for the
isotropic system. This indicates a quantitative difference of the multifractal
properties of states of the anisotropic as compared to the isotropic system.
Further, we calculate the Kubo conductivity for given anisotropies by exact
diagonalization. Already for small system sizes of only $12^3$ sites we observe
a rapidly decreasing conductivity in the directions with reduced hopping if the
coupling becomes weaker.
