This paper presents the results of numerical modeling of the spatial structure and saturation of Alfvén eigenmodes in the GLOBUS-M spherical tokamak with the KINX and VENUS codes. Measurements with the multichannel Doppler backscattering reflectometry provided experimental evidence of the mode localization near the plasma boundary when excited by energetic particles during neutral beam injection heating. The numerical results suggest the Alfvén-sound eigenmode, in particular the beta-induced Alfvén acoustic eigenmode, as the candidate instability responsible for the observed localization pattern. The mode linear growth rates and nonlinear saturation levels are found to be highly sensitive to the parameters of the model.