Abstract: An algorithm for the computation of the unstructured real stability radius of high dimensional linear system is presented. Using the accurate formula of the real stability radius of 2-dimensional system linear system checks the algorithm. The result shows that the algorithm is reliable and efficient. As applications, the unstructured real stability radii of 2-dimensional Chua's circuit and 3-dimensional piecewise-linear system are calculated, the dynamical orbits of the corresponding perturbed systems are simulated.