  Thermodynamic properties of strange quark matter in strong magnetic fields
$H$ up to $10^{20}$ G are considered within the MIT bag model at zero
temperature implying the constraints of total baryon number conservation,
charge neutrality and chemical equilibrium. The pressure anisotropy, exhibiting
in the difference between the pressures along and perpendicular to the field
direction, becomes essential at $H>H_{th}$, with the estimate
$10^{17}<H_{th}\lesssim10^{18}$ G. The longitudinal pressure vanishes in the
critical field $H_c$, which can be somewhat less or larger than $10^{18}$ G,
depending on the total baryon number density and bag pressure. As a result, the
longitudinal instability occurs in strange quark matter, which precludes: (1) a
significant drop in the content of $s$ quarks, which, otherwise, could happen
at $H\sim10^{20}$ G; (2) the appearance of positrons in weak processes in a
narrow interval near $H\sim2\cdot10^{19}$ G (replacing electrons). The
occurrence of the longitudinal instability leaves the possibility only for
electrons to reach a fully polarized state, while for all quark flavors the
polarization remains mild even for the fields near $H_c$. The anisotropic
equation of state is determined under the conditions relevant to the interiors
of magnetars.
