This technical note concerns the reach control problem for the dynamical systems represented by linear differential inclusions. The goal is to derive conditions for the trajectories of a differential inclusion defined on a full-dimensional simplex to reach exit facets in finite time using affine feedback. To achieve this goal, an invariance condition is firstly derived for Lipschitz differential inclusions. As an application of the obtained invariance condition, the reach control problem (RCP) is solved for two classes of differential inclusions: norm-bounded linear differential inclusion and polytypic linear differential inclusion, in the sense of strong and weak reachability, respectively.