  In the present work we study strange stars in $f(R)$ theories of gravity in
the Palatini formalism. We consider two concrete well-known cases, namely the
$R+R^2/(6 M^2)$ model as well as the $R-\mu^4/R$ model for two different values
of the mass parameter $M$ or $\mu$. We integrate the modified
Tolman-Oppenheimer-Volkoff equations numerically, and we show the mass-radius
diagram for each model separately. The standard case corresponding to the
General Relativity is also shown in the same figure for comparison. Our
numerical results show that the interior solution can be vastly different
depending on the model and/or the value of the parameter of each model. In
addition, our findings imply that i) for the cosmologically interesting values
of the mass scales $M,\mu$ the effect of modified gravity on strange stars is
negligible, while ii) for the values predicting an observable effect, the
modified gravity models discussed here would be ruled out by their cosmological
effects.
