Tsunami in the Indian Ocean generated by a strong earthquake in Sumatra-Andaman region on 26 December 2004 led as known to catastrophic results at the coast of many countries of this region. In spite of intensive study of this event by a number of groups, the character of seafloor displacements in the source during this earthquake remains to be controversial. In this work, it is performed an analysis of physical aspects of similar earthquakes on the basis of keyboard model of tsunamigenic earthquakes. The numerical simulation of generation, propagation and run-up of surface water waves on the basis of simplified keyboard model of tsunamigenic earthquakes with vertical displacements of keyboard blocks in approximative geometry (without taking into account the real bathymetry) is also performed. It is obtained that tsunami waves generated by various combinations of keyboard block displacements are essentially different in character which fact leads to quite different picture of maximum run-up distribution along the near-field coast. It is performed the estimative computation for 26 December 2004 Sumatra-Andaman earthquake with taking into account of oblique character of the subduction zone characteristic for this earthquake. The computations performed explain the complex character of run-up distribution at nearest to the source coasts and are in a good agreement with run-up values at the Thailand coast. It is noted that such a model can account for more adequately the tsunami wavefield character in another regions of the Indian and the Pacific Ocean basins as well.