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A well-posed stress-driven mixture is proposed for Timoshenko nano-beams.The model is a convex combination of local and nonlocal phases and circumvents some problems of ill-posedness emerged in strain-driven Eringen-like formulations for structures of nanotechnological interest. The nonlocal part of the mixture is the integral convolution between stress field and a biexponential averaging kernel function characterized by a scale parameter.The stress-driven mixture is equivalent to a di erential problem equipped with constitutive boundary conditions involving bending and shear fields.Closed-form solutions of Timoshenko nano-beams for selected boundary and loading conditions are established by an e ective analytical strategy. The numerical results exhibit a sti ening behavior in terms of scale parameter.