Due to size limits in the transverse direction, tensile testing is not appropriate to investigate the mechanical properties of elytra cuticle of the dung beetle (Copris ochus Motschulsky). However, nanoindentation testing can determine a material’s anisotropic properties through a single indentation. In the present study, nanoindentation stress–strain curves were used to characterize the complete mechanical behavior of dung beetle elytra cuticle. A differential constitutive equation has been developed with time-dependent spring constants k and viscosities η . To describe the complex viscoelastic behavior of dung beetle cuticle, a descriptive representation of the linear viscoelasticity law for the multilayer matrix has been formulated. A qualitative model for the relationship between cuticle structure and mechanical properties of elytra may help develop bionic composite materials for micro-aircraft, bionic tribology, bionic medical apparatus, and bionic organs (tissue engineering).