We perform direct 3-dimensional numerical simulations for magnetohydrodynamic
(MHD) turbulence in a periodic box of size $2\pi$ threaded by strong uniform
magnetic fields. We use a pseudo-spectral code with hyperviscosity and
hyperdiffusivity to solve the incompressible MHD equations. We analyze the
structure of the eddies as a function of scale. A straightforward calculation
of anisotropy in wavevector space shows that the anisotropy is scale-{\it
independent}. We discuss why this is {\it not} the true scaling law and how the
curvature of large-scale magnetic fields affects the power spectrum and leads
to the wrong conclusion. When we correct for this effect, we find that the
anisotropy of eddies depends on their size: smaller eddies are more elongated
than larger ones along {\it local} magnetic field lines. The results are
consistent with the scaling law $\tilde{k}_{\parallel} \sim
\tilde{k}_{\perp}^{2/3}$ proposed by Goldreich and Sridhar (1995, 1997). Here
$\tilde{k}_{\|}$ (and $\tilde{k}_{\perp}$) are wavenumbers measured relative to
the local magnetic field direction. However, we see some systematic deviations
which may be a sign of limitations to the model, or our inability to fully
resolve the inertial range of turbulence in our simulations.