  We study vacuum in a strong magnetic field. It shows a nonlinear response, as
a ferromagnetic medium. Anisotropic pressures arise, and a negative pressure is
exerted in the direction perpendicular to the field. The analogy of this effect
with the Casimir effect is analyzed. The vacuum transverse pressure is found to
be of the same order of the statistical pressure for $B\sim10^{15}G$ and
$N\sim10^{33}electrons/cm^{3}$. Vacuum interaction with the field is studied
also for $B\sim10^{16}G$ and larger, including the electron anomalous magnetic
moment. We estimate quark contribution to vacuum behavior.
