<p>This study presents a comprehensive analytical–numerical framework for characterizing the progressive contact phenomena in direct disc tests, with a specific focus on radial compression configurations. By formulating and solving a dual trigonometric series representation of the contact problem, the model enables precise determination of contact pressure distributions, angular extents, and the ensuing load–displacement relationships. The proposed analytical methodology is rigorously validated against finite element method (FEM) simulations, demonstrating close quantitative agreement across a range of load levels. Under the radial compression, strong correspondence between analytical and FEM results is revealed, with a peak load and displacement of 16.710 kN and 0.00070 mm, compared to 17.806 kN and 0.00076 mm from the FEM, reflecting a variation of about 6.155% under the same load increment.&#xa0;The comprehensive stress analyses underscore the comparability of maximum tensile stresses at the disc center derived from approaches, confirming the validity and predictive reliability of the presented model. Furthermore, the markedly lower failure loads associated with radial compression conditions highlight their suitability for testing protocols employing lower-capacity equipment. Overall, this research significantly augments the current understanding of contact mechanics in ring-based disc tests, promoting enhanced accuracy, versatility, and applicability in experimental and computational rock mechanics investigations.</p>