Ellipsoidal Toolbox (ET) implements in MATLAB the ellipsoidal calculus and its application to the reachability analysis of continuous- and discrete-time, possibly time-varying linear systems, and linear systems with disturbances, for which ET calculates both open-loop and close-loop reach sets. The ellipsoidal calculus provides the following benefits: The complexity of the ellipsoidal representation is quadratic in the dimension of the state space, and linear in the number of time steps; it is possible to exactly represent the reach set of linear system through both external and internal ellipsoids; it is possible to single out individual external and internal approximating ellipsoids that are optimal to some given criterion (e.g. trace, volume, diameter), or combination of such criteria; it gives simple analytical expressions for the control that steers the state to a desired target.