We perform direct three-dimensional numerical simulations for magnetohydrod
ynamic (MHD) turbulence in a periodic box of size 2 pi threaded by strong u
niform magnetic fields. We use a pseudospectral code with hyperviscosity an
d hyperdiffusivity to solve the incompressible MHD equations. We analyze th
e structure of the eddies as a function of scale. A straightforward calcula
tion of anisotropy in wavevector space shows that the anisotropy is scale i
ndependent. We discuss why this is not the true scaling law and how the cur
vature 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 elongat
ed than larger ones along local magnetic held lines. The results are consis
tent with the scaling law (k) over tilde(//) similar to (k) over tilde(perp
endicular to)(2/3) recently proposed by Goldreich & Sridhar. Here (k) over
tilde(//) (and (k) over tilde(perpendicular to)) are wavenumbers measured r
elative to the local magnetic held direction. However, we see some systemat
ic deviations that may be a sign of limitations to the model or our inabili
ty to fully resolve the inertial range of turbulence in our simulations.