  We construct an equation of state of strange quark matter in strong magnetic
field within a confining model. The confinement is modeled by means of the
Richardson potential for quark-quark interaction modified suitably to account
for strong magnetic field. We compare our results for the equation of state and
magnetization of matter to those derived within the MIT bag model. The
differences between these models arise mainly due to the momentum dependence of
the strong interaction between quarks in the Richardson model. Specifically, we
find that the magnetization of strange quark matter in this model has much more
pronounced de Haas-van Alf\'{v}en oscillations than in the MIT bag model, which
is the consequence of the (static) gluon-exchange structure of the confining
potential.
