A certain analysis of free vibration frequencies of a plate band with a smooth and a slow gradation of properties on the macro-level is made in this article. These plate bands have a tolerance-periodic structure on the micro-level. Hence, it can be shown that for such objects the effect of the microstructure size plays a crucial role in dynamic problems, cf. Jędrysiak [2009], Kaźmierczak and Jędrysiak [2011]. In order to describe this effect the tolerance model of these bands is applied in this paper. Moreover to evaluate obtained results the asymptotic model is used. Fundamental free vibrations frequencies of the plate band, using the Ritz method are calculated using these models. Higher free vibrations frequencies are also obtained in the framework of the tolerance model. Moreover the effect of differences of Young’s modulus and of mass densities in the cell on the microlevel is shown.

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