<p>Most of the existing computational models for the analysis of beam structures undergoing large deformations are based on the hypothesis of small strains. In this paper, we present a finite-strain, geometrically-exact beam formulation suitable for visco-hyperelastic materials. Three-dimensional constitutive equations are expressed starting from the stored energy function, which is split into hyperelastic and dissipative contributions. We employ a linearized evolution law that permits expressing the rate-dependent strains in terms of the one-dimensional geometrically exact strain measures. High efficiency is pursued discretizing the governing equations using the isogeometric collocation (IGA-C) method. Numerical examples demonstrate the distinctive ability of the proposed model to reproduce the beam rate-dependent response in a context where large deformations and finite-strains coexist.</p>