In this investigation, a solution model is proposed to characterize and analyze the stresses and displacements induced by surface waves in a corrugated, inhomogeneous, fibre-reinforced material under magneto-elastic influences, with some underlying mechanical inclinations. The governing equations of the model problem are presented using the material's constitutive relations. By the normal mode method, we derived the analytical solution of the model whilst utilizing non-dimensionalization of the equations of motion to reduce redundant parameters, and so on. Also, the model considers only a case in which the boundary corrugation or wavy-like phenomenon has various amplitudes and inhomogeneous impedance conditions, resulting in a complex geometry. Following this, suitable applications of the formulated boundary conditions – variable-amplitude corrugation and inhomogeneous impedance conditions, along with mechanical inclinations - are used to ensure that the complete solutions for the wave's stresses and displacements in the inhomogeneous medium are derived. In addition, the distributions of stresses and displacements in these fields are graphically presented using MATHEMATICA software to assess the variations and behaviors of the considered physical quantities, including the nonlocal parameter, variable-amplitude corrugation, inhomogeneous impedance parameters, and angles of inclination. We observe that these parameters significantly affect the distribution of the surface wave across the material, with the nonlocal, angle-of-inclination, and inhomogeneous parameters causing downward trends in the distribution profiles as they increase. Exceptional cases of constant amplitude can be obtained from our model if we neglect one of the quantities with variable amplitude in the corrugation and the magnetic impact on the medium. This study should prove helpful for examinations in geophysics and seismology, where the analysis of surface disturbances is required.