In this paper, problem of reachable sets bounding is considered for switched neural networks systems with mixed time-varying delays and bounded disturbances. By using Lyapunov–Krasovskii functional method, some new sufficient conditions are derived for the existence of (1) the smallest possible outer bound of forwards reachable sets; and (2) the largest possible inter bound of backward reachable sets. These conditions are delay dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. A constructive geometric design of switching laws is also presented. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.