SUMMARYIn this paper, hybrid-mixed elements for static and vibration analyses of curved beams are presented. The proposed elements based on the Hellinger-Reissner variational principle employ the consistent stress parameters corresponding to the displacement fields with additional internal nodeless degrees of freedom in order to enhance the numerical performance. Elimination of the stress parameters by the stationary condition and condensation of internal nodeless degrees of freedom by Guyan reduction are carried out in the element formulation. This study shows how much the order of internal nodeless displacement functions and the type of mass matrix affect the numerical performance of hybrid-mixed curved beam elements in static and dynamic analyses. Various numerical examples confirm that the proposed elements with increased internal nodeless degrees of freedom generate superior accuracy in the prediction of bending behaviours and high vibration modes.