<p>This paper presents a novel surface model based on the Gurtin–Murdoch theory and Kerr-type differential relations, which is established and numerically simulated. By employing the principles of equivalent force and mechanical equilibrium, a differential equation for the contact pressure-deflection relationship between a rigid indenter and an elastic thin beam is derived. The study investigates pressure distribution within the contact area and deformation patterns outside this region. The relationship between indentation parameters is analyzed from two perspectives: clamped and simply-supported boundaries, with a detailed comparison to classical cases. The findings reveal that the normalized contact pressure and load–displacement relationship of elastic thin beams are influenced not only by the half-width ratio and indentation depth but also by the material’s surface elasticity. Similar to classical contact scenarios, an increase in surface elasticity leads to the separation of the indenter from the beam’s center when the contact half-width exceeds a certain threshold (e.g., a ratio of 4 to the beam thickness). This results in a negative normalized contact pressure and the formation of two independent, symmetric contact strips. Notably, the relationship between displacement and contact half-width remains largely unaffected by surface elasticity, aligning with classical indentation contact results. The methodology and outcomes of this research provide a foundation for analyzing the structures and properties of nanostructured materials, offer insights for the design of future nanostructured devices, and present innovative approaches to addressing practical engineering challenges.</p>