In this paper, motivated by a $$\tau $$
τ
-tilting version of the Brauer-Thrall Conjectures, we study general properties of band modules and their endomorphisms in the module category of a finite dimensional algebra. As an application we describe properties of torsion classes containing band modules. Furthermore, we show that a special biserial algebra is $$\tau $$
τ
-tilting finite if and only if no band module is a brick. We also recover a criterion for the $$\tau $$
τ
-tilting finiteness of Brauer graph algebras in terms of the Brauer graph.