The aftershock processes that occurred in 1990–2008 on the Kamchatka Peninsula and in the adjacent water area are numerically modeled with the aim of forecasting the aftershock activity. The aftershocks are identified by the Molchan-Dmitrieva algorithm followed by the analysis of spatiotemporal distribution of the earthquakes, which gives the final aftershock sequences. The simulations are based on the relaxation and triggering models of the aftershock processes. The studied models adequately describe and reliably simulate the temporal behavior of the aftershock sequences. An attempt is made to forecast the aftershock processes in Kamchatka using the ETAS model. It is shown that forecasting based on the data observed during the preceding time intervals is quite accurate. This approach can be applied in the centers of seismological monitoring for estimating the aftershock activity within the first days after a strong earthquake.