The problem of intercepting a ballistic missile optimally at moderate range is discussed. The problems of minimum time and minimum fuel consumption are specifically reported. A procedure is given for determining the trajectory on a digital computer, and some necessary and sufficient conditions are given for the corresponding optima. The computational procedure is a method of successive approximations. The simpler cases were checked out on the digital computer and further programming is under way. In the examples run, each iteration takes somewhat less than one second computing time on the CDC 1604. From three to six iterations are usually required to determine a trajectory, so that the trajectory is determined in five seconds or so. The variational equations, used to determine the trajectory, can also be used to determine the corrective thrust should the actual trajectory deviate slightly from the planned trajectory.