Numerical experiences with a method for the approximation of reachable sets of nonlinear control systems are reported. The method is based on the formulation of suitable optimal control problems with varying objective functions, whose discretization by Euler's method lead to finite dimensional non-convex nonlinear programs. These are solved by a sequential quadratic programming method. An efficient adjoint method for gradient computation is used to reduce the computational costs. The discretization of the state space is more efficiently than by usual sequential realization of Euler's method and allows adaptive calculations or refinements. The method is illustrated for two test examples. Both examples have non-linear dynamics, the first one has a convex reachable set, whereas the second one has a non-convex reachable set.