In many structural applications like bridges, arches, etc., frames are used, and it is important to study their dynamic behavior. Finite element method (FEM) is usually used for computational simulation of vibration for such frame structures. However, FEM simulations for high frequency are computationally intensive and lack accuracy. This paper proposes a wave propagation-based approach for the vibration analysis of a frame having angular and curved joints. The reflection and transmission matrices for the joints are derived using the kinematic compatibility and equilibrium conditions. Reflection, transmission, and propagation matrices are assembled leading to matrix equation terms of the wave amplitudes. Modal analysis and harmonic analysis of frames having curved and angular joints are performed using the present formulation. The frequency response function for point harmonic forcing acting on such structures is also presented. The formulation and the results are non-dimensionalized for wider applicability. The results obtained using the present formulation are compared with those obtained through FEM simulation in a commercial package. It is found that the results obtained using the two methods are in excellent correlation. The computational efficiency of the present method over FEM simulation is also reported.