  The present work investigates the gravitational collapse of a perfect fluid
in $f(R)$ gravity models. For a general $f(R)$ theory, it is shown analytically
that a collapse is quite possible. The singularity formed as a result of the
collapse is found to be a curvature singularity of shell focusing type. The
possibility of the formation of an apparent horizon hiding the central
singularity depends on the initial conditions.
