  One of the most important problems in hybrid systems is the {\em reachability
problem}. The reachability problem has been shown to be undecidable even for a
subclass of {\em linear} hybrid systems. In view of this, the main focus in the
area of hybrid systems has been to find {\em effective} semi-decision
procedures for this problem. Such an algorithmic approach involves finding
methods of computation and representation of reach sets of the continuous
variables within a discrete state of a hybrid system. In this paper, after
presenting a brief introduction to hybrid systems and reachability problem, we
propose a computational method for obtaining the reach sets of continuous
variables in a hybrid system. In addition to this, we also describe a new
algorithm to over-approximate with polyhedra the reach sets of the continuous
variables with linear dynamics and polyhedral initial set. We illustrate these
algorithms with typical interesting examples.
