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Here, we consider the problem of twisting of a cylindrical bar of elliptic cross-section. The bar is assumed to consist of a nonlinear viscoelastic material (NVeM). In addition, we consider the bar is subjected to nobody forces and free from forces acting on its lateral surface. Under certain conditions, the problem yields to a nonlinear Volterra integral equation (NVIE) of the second kind. The existence and uniqueness of solution of the integral equation is considered. Moreover, the bestdoi:10.21172/ijiet.84.008 fatcat:4kz4p4tqyvbcvjviouy5grhuki