The rupture directivity for the 2004 Sumatra earthquake is analyzed by examining differences between the phase-delay times of Rayleigh-waves (in the 140 - 160 sec period range) arising from the main shock and reference earthquakes. A long source-process time (~463.0 sec) and large rupture length (~1164.0 km) are derived from this analysis of rupture directivity. The source-process time for this earthquake is larger than for either the 1960 Chile or 1964 Alaska earthquakes. This might be due to the length of the rupture that occurred during earthquake faulting. The estimated rise time for the 2004 Sumatra earthquake, 92.0 sec, is approximately 20% of the whole source duration and also larger than those for the 1960 Chile and 1964 Alaska earthquakes. This likely reflects a fundamental difference between the frictional properties of these earthquakes. When the rise time is taken into account, an estimated rupture velocity of approximately 3.1 km sec^-1 is obtained. This value is higher than that found in previous studies carried out on the basis of hydro acoustic data and regional seismic net works. In this study, we obtain additional evidence from analysis of the surface-wave phase-delay time which con firms the basic features of the rupturing of the 2004 Sumatra earthquake. The results can also provide some constraints for the study of source rupturing for this earthquake.