To dynamically model slender structures conveniently by Cosserat rod theory, the dynamic equations for pre-stressed curved Cosserat rods are established within the framework of this rod theory by defining variables to describe their initial configurations, their pre-stresses and their initial deformations, which move along with their cross sections. Based on their corresponding specific assumptions, the dynamic equations for a cable with initial sag and a circular arch beam, which have wide applications in bridge structures, are explored within the framework of pre-stressed curved Cosserat rods, respectively. The results are in agreement with their corresponding equations obtained by other methods in references. Since the Cosserat theory is geometrically exact, the dynamic equations for pre-stressed curved Cosserat rods derived here are not only retaining all geometric nonlinear characteristics but also of universality, which can be effectively and efficiently exploited to nonlinear dynamically model for slender structures in practical engineering situations.