<p>A hybrid spectral-element spectral-integral (SESI) method is proposed to model elastic wave scattering in one-dimensional Bloch-periodic problems involving two-dimensional scatterers embedded in layered media. The method combines the spectral element method (SEM) and the spectral integral method (SIM), in which the computational domain is partitioned into SEM subdomains containing scatterers and SIM subdomains representing purely layered media. The SIM, based on the periodic layered medium Green’s function (PLMGF), provides an exact radiation boundary condition for the upper and lower boundaries of SEM subdomains, thereby eliminating the need for discretization in the layered media. Owing to its exponential convergence at low sampling densities, SEM outperforms the traditional finite element method (FEM), while SIM further enhances efficiency by avoiding discretization of the piecewise homogeneous layered media and rapidly evaluating the field through PLMGF. Consequently, the SESI method achieves higher accuracy and efficiency than SEM or FEM alone. Four numerical experiments verify the proposed approach, demonstrating both the accuracy of the SIM formulation and the superiority of SESI over SEM and FEM. These results highlight SESI as a promising tool for the design and optimization of phononic crystals, elastic metamaterials, and metasurfaces.</p>