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A mathematical model analyzing the effects of initial stress and variable amplitudes of corrugation for stresses and displacements of surface waves on a fiber-reinforced half-space under a magnetic field and inhomogeneous impedance existing as a linearly varying impedance is proposed. Constitutive equations of homogeneous fiber-reinforced material are utilized in formulating the dynamical equations while incorporating the components of the magnetic field owing to Maxwell's theory of electromagnetism. The normal mode method paved the way in deriving the analytical solution vis-à-vis the stresses and displacements after suitable boundary conditions in terms of linearly varying impedance and linearly varying amplitudes of corrugation (existing as trigonometric Fourier series of diverse heights) were formulated and utilized. Utilizing Mathematica 11, derived stresses and displacements were graphically presented, thus demonstrating the variations of the interacting physical parameters of initial stress, variable amplitudes of corrugation, magnetic fields, and the inhomogeneous impedance. The combined fields' quantities of the model such as the linearly varying impedance and amplitudes of corrugated surface, magnetic field, and initial stress exhibited enormous physical influences on the stresses and displacements of the surface waves on the material. The gradient factor associated with the linearly varying impedance results to a decrease in the behavior of the stresses and displacements on the material when increased. However, an increase in one of the parameters associated with variable amplitudes of corrugation caused an upward trend in the stresses and displacements of the waves. Particular cases are observed from the literatures if we neglect some parameters of variable amplitudes and impedance. Received: 1 October 2025 | Revised: 21 January 2026 | Accepted: 27 February 2026 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement The data for fibre-reinforced material in this study is taken from published work Othman et al. [19]. Data is available on the Computational Results and Discussion section. Author Contribution Statement Augustine Igwebuike Anya: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing, Visualization, Supervision, Project administration. Ugochukwu David Uche: Methodology, Software, Validation, Data curation, Writing - review & editing, Visualization, Supervision, Project administration.