The stiffness problem in reactor kinetics is overcome by the stiffness confinement method for solving the kinetic equations. The idea is based on the observation that the stiffness characteristic is present only in the time response of the prompt neutron density, but not in that of the delayed neutron precursors. The method is, therefore, devised to have the stiffness decoupled from the differential equations for precursors and confined to the one for the prompt neutrons, which can be analytically solved. Numerical examples of applying the method to a variety of problems confirm that the time step increment size can be greatly increased and that much computing time can be saved, as compared to other conventional methods. The theory is of general validity and involves no approximation other than the discretization of the time variable.