The problem of seismic protection from the main types of surface acoustic waves and shear-pressure (SP) evanescent waves emanating from vicinity of an epicenter of an earthquake is discussed. Herein, SP waves represent a kind of the evanescent waves arising at critical angles of incident of bulk shear waves. The proposed seismic protection method utilizes vertical trenches (vertical barriers) filled with the specially constructed granular metamaterials. Some of nonlinear hyperelastic models along with nonlinear and inelastic models are analyzed for applications using granular metamaterials in case of cyclic dynamic loadings that correspond to arrival of the large intensity surface acoustic and evanescent waves. The main attention is paid to arrival of the large intensity Rayleigh, Rayleigh-Lamb and SP waves, as the most frequent waves and the most dangerous waves for engineering structures. Some of the new constitutive equations for metamaterials exhibiting different elastic moduli at tension and compression phases are proposed and discussed.