We model the dynamic behavior of laminated curved beams on the assumption that the different layers of such structures are perfectly bonded at the interface and can show different flexural rotations from one another. We formulate a mechanical theory and a finite element model accounting for bending, shear, warping and extensional deformation modes, as well as radial, tangential and rotary inertias. The main novelty of the proposed theory consists of a generalization of layer-wise displacement approaches available in literature to the dynamics of beams with finite curvature. The work includes some numerical results related to the free vibration of laminated arches and showing different support conditions and aspect ratios to establish comparisons with different theories in the literature. We observe that an accurate mechanical modeling of curved laminated beams is crucial for correct estimation of the eigenfrequencies and eigenmodes of such structures within a 1D framework.