  Let $\Lambda$ be an Artin algebra. In 2014, T. Adachi, O. Iyama and I. Reiten
proved that the torsion funtorially finite classes in $\mathrm{mod}\,(\Lambda)$
can be described by the $\tau$-tilting theory. The aim of this paper is to
introduce the notion of $F$-torsion class in $\mathrm{mod}\,(\Lambda)$, where
$F$ is an additive subfunctor of $\mathrm{Ext}^1_\Lambda,$ and to characterize
when these clases are preenveloping and $F$-preenveloping. In order to do that,
we introduce the notion of $F$-presilting $\Lambda$-module. The latter is both
a generalization of $\tau$-rigid and $F$-tilting in $\mathrm{mod}(\Lambda).$
