We investigate the global large amplitude waves propagating across the solar disk as observed by the SOHO/Extreme Ultraviolet Imaging Telescope (EIT). These waves appear to be similar to those observed in H&agr; in the chromosphere and which are known as Moreton waves, associated with large solar flares [Moreton, 1960, 1964>. Uchida [1968> interpreted these Moreton waves as the propagation of a hydromagnetics disturbance in the corona with its wavefront intersecting the chromosphere to produce the Moreton wave as observed in movie sequences of H&agr; images. To search for an understanding of the physical characteristics of these newly observed EIT waves, we constructed a three-dimensional, time-dependent, numerical magnetohydrodynamic (MHD) model. Measured global magnetic fields, obtained from the Wilcox Solar Observatory (WSO) at Stanford University, are used as the initial magnetic field to investigate hydromagnetics wave propagation in a three-dimensional spherical geometry. Using magnetohydrodynamic wave theory together with simulation, we are able to identify these observed EIT waves as fast mode MHD waves dominated by the acoustic mode, called magnetosonic waves. The results to be presented include the following: (1) comparison of observed and simulated morphology projected on the disk and the distance-time curves on the solar disk; (2) three-dimensional evolution of the disturbed magnetic field lines at various viewing angles; (3) evolution of the plasma density profile at a specific location as a function of latitude; and (4) computed Friedrich's diagrams to identify the MHD wave characteristics. ¿ 2001 American Geophysical Union