The arrivals of high intensity seismic Rayleigh and Rayleigh - Lamb waves to the buildings and structures with a relatively large footprint are analysed. The most frequent cases of the foundation structures' fracture and damage are discussed. The methods for seismic protection from the main types of surface seismic waves, Rayleigh, Rayleigh - Lamb, Love and some more peculiar evanescent (head) waves are considered. The analytical and numerical methods for modelling interaction of building structures with these types of surface seismic waves are analysed. The comparative analysis of the wave dynamic method and the methods based on the spectral decomposition is given.