We present a technique for overestimating the reachable set from the origin for a class ofn-dimensional linear control systems. The proposed ‘box’ method is based upon decomposing the system into one and two-dimensional subsystems for which bounds on the new variables can readily be found. Using these bounds enables the construction of an-dimensional parallelepiped containing the reachable set of the original system. Examples of this procedure are given as well as a comparison to an overapproximation afforded by a Lyapunov approach.