In this paper, a general wave propagation approach for the vibration analysis of three-dimensional waveguide structures is presented. The analysis is based on a ray tracing method that considers wave propagation and scattering in the formulation, including the effects of decaying near-field wave components. The waveguide dispersion characteristics of straight and curved beams, which govern the propagation and decay of waves as they travel through the different components, are taken into account for different wave types (flexural, torsional, and axial). Separate elements are coupled using reflection and transmission coefficients, and these are derived for a general connection between several non-planar elements. A matrix formulation is used that offers an automatic and concise method for tackling free and forced vibrations problems of complex ring-beam structural systems. The general methodology is demonstrated on simple applications, and the predictions made using the proposed approach are shown to be in excellent agreement with a conventional finite element analysis, with the advantage of reduced computational costs.