Linear hybrid systems are dynamical systems whose variables change both discretely and continuously along piecewise linear trajectories; they are useful for modeling digital real-time programs that are embedded in analog environments. Model checking is an algorithmic technique for anlayzing finite- state systems that has recently been extended to certain infinite-state systems, including linear hybrid systems. The method has been implemented in HyTech (The Cornell Hybrid Technology Tool), a symbolic model checker for linear hybrid systems. We report on a new implementation and several experiments with HyTech. The core of HyTech is a semidecision procedure that, given a linear hybrid automaton describing a system and a temporal formula describing a requirement, computes the so-called target region-the linear set of system states that satisfy the requirement. Unfortunately, the verification procedure may not return the target region using a reasonable amount of time and space, or it may not terminate in principle. Thus we have reimplemented the model checker using more efficient data structures that represent linear state sets geometrically, as unions of convex polyhedra, and we have experimented with several strategies that are designed to improve the performance of the model checker further: we (1) simultaneously compute the target region from different directions, (2) encode data as finite-state control, (3) approximate the target region by dropping constraints, and (4) iteratively refine the approximation until sufficient precision is obtained. Interestingly, symbolic model checking (fixpoint computation by iteration) and the polyhedral approximation strategies (3) can be viewed as the abstract interpretation of linear hybrid systems.