We investigate three available coseismic fault models of the 2006 M7.8 Java tsunami earthquake, as reported by Fujii and Satake (2006), Bilek and Engdahl (2007), and Yagi and Fukahata (2011), in order to find the best coseismic model based on mechanisms of postseismic deformation associated with viscoelastic relaxation and afterslip. We construct a preliminary rheological model using vertical data, obtaining a final rheological model after we include horizontal and vertical components of afterslip in the further process. Our analysis indicates that the coseismic fault model of Fujii and Satake (2006) provides a better and more realistic result for a rheological model than the others. The best-fit rheological model calculated using the coseismic fault model of Fujii and Satake (2006) comprises a 60±5km elastic layer thickness with a viscosity of 2.0±1.0×1017Pas in the asthenosphere. Also, we find that afterslip is dominant over the horizontal displacements, while viscoelastic relaxation is dominant over the vertical displacement. Additionally, in comparison to the coseismic displacement found through GPS data taken at BAKO station, our calculation indicates that Fujii and Satake (2006) modeled coseismic displacements with less GPS data misfit than the other examined models. Finally, we emphasize that our methodology for evaluating the best coseismic fault model can satisfactorily explain the postseismic deformation of the 2006 Java tsunami earthquake.