Brake squeal in heavy-duty S-cam drum brakes remains a persistent NVH challenge, primarily driven by friction-induced modal instabilities. Existing studies on drum brake squeal mitigation largely emphasize geometric modifications, stiffness tuning, or the application of damping treatments, while the influence of directional stiffness characteristics of friction linings remains insufficiently explored. This research presents a novel, material-centric approach by modelling the brake lining as a transversely isotropic material, characterized by six independent elastic constants, and systematically quantifying their influence on squeal-prone unstable modes using Complex Eigenvalue Analysis (CEA). A validated finite-element model of a production S-cam drum brake assembly is developed and correlated through experimental modal analysis, ensuring close agreement between predicted and measured natural frequencies and mode shapes. The validated model is then integrated with a Design of Experiments (DOE) within commercially available FEA software to quantify both main effects and higher-order interactions across practical ranges of in-plane and out-of-plane elastic moduli and shear constants. To enhance the predictive accuracy of the surrogate models, a subsequent sampling–fit study is conducted, significantly improving the coefficient of determination (R2) of the response surfaces. The refined surrogate models are employed within a Global Response Surface Methodology (GRSM) framework to perform multi-parameter optimization aimed at minimizing squeal propensity under representative operating conditions. Finally, complex eigenvalue analysis quantifies the impact of the optimized transversely isotropic property combinations on modal stability, establishing a predictive, optimization-driven methodology for robust, noise-free drum brake design. The study culminates in the identification of an optimized transversely isotropic elastic-constants signature for the friction lining, providing actionable targets for friction material formulation and reinforcement alignment. Unlike prior research focused on isotropic material assumptions or component-level design changes, this first-of-its-kind methodology advances the state of the art by enabling friction material– centric NVH optimization for heavy-duty drum brake systems.