SummaryThis work introduces a semi‐analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate that enlarges, shrinks, or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems, computations are performed in the frequency domain. Results of this work are validated using the global matrix method and standard finite element analysis. Copyright © 2016 John Wiley & Sons, Ltd.