The physical mechanism of deep earthquakes can be constrained by identifying their fault planes. Resolving the fault plane ambiguity is a classical problem in seismology, and we present a method to distinguish the fault plane using observations of source finiteness. Source finiteness is observable on seismograms at different azimuths and distances, for single-event ruptures, as variations in the apparent rupture duration and, for complex ruptures, as differences in the traveltime delay between subevents. For each earthquake, the rupture duration (or traveltime delay) will be shortest in the direction of rupture propagation and longest in the opposite direction. Rather than measuring the actual rupture duration at each station, we use a cross-correlation technique that includes a stretching factor to measure the differential rupture duration between each pair of stations. These differential measurements then allow us to identify the rupture direction, rupture velocity, and fault plane for each earthquake. First, we test the method on two synthetic earthquakes, which represent earthquakes composed of one and two events. The method works well for both examples, although attenuation can bias the determined rupture direction for the single-event case. Next, we apply this method to P waves from broadband seismograms from four intermediate- and deep-focus earthquakes composed of two subevents: the 23 January 1997 Bolivian earthquake (MW 7.1, 276 km depth), the 27 October 1994 earthquake south of the Fiji Islands (MW 6.7, 549 km depth), the 21 July 1994 Japan Sea earthquake (MW 7.3, 471 km depth), and the 11 November 1998 Fiji Islands earthquake (MW 6.3, 149 km depth). Each focal mechanism contains a subvertical and a subhorizontal nodal plane. For three of the events, our analysis shows that rupture propagated subhorizontally, and we identify the subhorizontal nodal plane as the fault plane. For the smallest event, the rupture azimuth, but not the rupture dip, is well constrained, and we cannot conclusively identify the fault plane. Rupture velocities vary from 0.18 to 0.63 of the local P wave velocity.