<p>This study investigates the characteristics of SH waves propagating through a viscous fluid-coated slope. The incident SH wave in the viscous fluid layer is derived using the Navier–Stokes equations. Subsequently, the standing wave within the slope is analytically expressed through fractional Bessel function expansion and Graf’s addition theorem. To analyze wave scattering, the large-arc assumption method is employed, segmenting the elastic half-space and viscous fluid layer along a horizontal interface. Straight boundaries are transformed into curved ones, and the resulting scattered wave expressions are formulated. Boundary conditions yield integral equations, which are solved via orthogonal function expansion and controlled truncation. Numerical results assess the dynamic stress concentration factor at the lower interface of the slope. Additionally, analytical solutions are validated against finite element simulations to confirm the study’s accuracy.</p>