The logic of Bunched implications (BI), and its boolean version (Boolean BI), are logics that allow us to express properties on resources and to provide logical frameworks for the so-called separation logics. In this paper we study a new modal separation logic that extends Boolean BI with two kinds of modalities, in order to deal with resources having dynamic properties (which depend on the current state of a system) and also to capture some resource evolutions or transformations. We show how we can model concurrent processes manipulating resources, and we provide a sound and complete tableau calculus, with a counter-model extraction method, for proving properties expressed in this logic.