In the article a conceptual approach towards the computation of polyhedral approximations of the reachable set of an impulsive dynamic control system is presented. This method consists in computing a sufficiently large number of points close to the boundary of the reachable set by regarding each one as the value at the final time of the optimal state trajectory for an optimal impulsive control problem with a certain linear cost functional. The iterative algorithm used to solve the optimal impulsive control problem involves its implicit transformation into a conventional one by the so called reduction transformation method. The auxiliary reduced problem is solved by an improvement algorithm based on local approximations to the reachable set.