Some temporal properties of reactive systems, such as actions with duration, accomplishments, and temporal aggregations, which are inherently interval-based, can not be properly dealt with by the standard, point-based temporal logics LTL, CTL and CTL*, as they give a state-by-state account of system evolution. Conversely, interval temporal logics-which feature intervals, instead of points, as their primitive entities-are highly expressive formalisms for temporal representation and reasoning that naturally allow one to deal with them. In this paper, we study the model checking (MC) problem for Halpern and Shoham's modal logic of time intervals (HS), interpreted on Kripke structures, under the homogeneity assumption, according to which a proposition letter holds over a finite computation path (interval) if and only if it holds at all of its states. HS is the best known interval-based temporal logic, which has one modality for each of the 13 possible ordering relations between pairs of intervals (the so-called Allen's relations), apart from equality. We focus on the MC problem for some HS fragments featuring modalities for (a subset of) Allen's relations meet, met-by, started-by, and finished-by, showing that it is in P NP , a class to which other pointbased logics (e.g., CTL+ and FCTL) are known to belong. Additionally, we provide some complexity lower bounds to the problem. All the algorithms we propose can be efficiently implemented by means of a polynomial-time procedure which iteratively invokes a SATsolver, enabling us to directly exploit the great speed of SAT-solvers.