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Recently the materials possessing structure of molecular and supramolecularmatrix are more and more actively studied. They are relative to many polymericmaterials of a technological origin, such as rubber, and living biologicaltissues. Processes of mechanical deformation of these continuous media havepeculiarities connected, first, with accounting for internal friction anddissipation of energy, and secondly, with nonlinearity of their elastic andviscous properties, that is with violation of Hook and Newtons laws.Traditional approaches to mechanics of viscoelastic bodies sometimes areexcessively difficult, and more evident and available representations arenecessary. The invaluable role in studying of the operating processesmechanisms of elastic deformation and motility of biological materials isplayed by the mathematical modeling. New effect obtained by means of computerexperiment of nonmonotonic relaxation of deformation in heterogeneous media isconsidered in the present work. Rheological properties of described media aregoverned by the differential equations of the first order on time (theevolution equations), as well as a huge variety of other physical processes.The physical phenomena in nonlinear systems with dissipation have a bigcommunity, including such it would seem far areas, as dynamics of magnetizationin ferrite. Therefore the problem of studying new effects of viscous frictionin the conditions of nonlinearity and heterogeneity, is very actual as inrespect of fundamental research nonlinear and non-uniform environments, and inmany areas of materials science, design of new materials, engineering ofbiological substitutes of living tissues and development of the micromagneticdevices using essentially new opportunities.

Nonmonotonic Relaxation as a Result of Spatial Heterogeneity in the Model of In-series Blocks Chain