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The non-linear elastic properties of rock samples and metal samples of microcrystalline aluminium alloy were studied using NRUS method. The residual shear strains were initially introduced in metal samples. In these samples the effect of slow dynamics was also investigated. Based on the analysis of experimental results it was concluded: the effect of slow dynamics, observed in the experiment, can not be explained solely by thermoelastic effects, but it is associated, in our opinion, with the slow relaxation of the internal structure of the samples. doi:10.1088/1757-899X/42/1/012029