This paper presents a finite-element formulation for the dynamic analysis of I-beams curved in-plan, in which geometric nonlinearities owing to large deflections and inelastic material behavior are taken into account. The developed finite element is based on the total Lagrangian formulation. Wagner and warping effects are considered in the analysis. The nonlinear dynamic equilibrium equations are solved by using Newmark's step by step numerical integration procedure. The von Mises associative isotropic hardening model is used to formulate the metal plasticity. The elastic predictor-radial corrector algorithm is used to consider gradual yielding on the cross section and along the beam. Simpler finite-element formulations are also developed by excluding the effects of geometric and material nonlinearities. Numerical examples are provided to illustrate the significance of the effects of geometric and material nonlinearities on the dynamic behavior of I-beams that are curved in-plan.