This work investigates a two mass–spring–damper system incorporating frictional resistance and interfacial adhesion, extending classical detachment models to a more realistic framework. The dynamics of the system are governed by a highly nonlinear set of ordinary differential equations, combining Coulomb dry friction with adhesion-induced bonding forces. We analyze the resulting model and establish key theoretical properties, including existence, uniqueness, and convergence of both continuous and discrete approximations. To address the intrinsic non-smoothness and strong nonlinearity arising from friction and adhesion effects, we develop stable numerical schemes based on regularization techniques and Newton–Raphson iterations. Numerical experiments demonstrate adhesion-dependent detachment behavior, capturing the initiation and evolution of detachment processes. These results not only validate the analytical findings but also provide deeper insight into the interplay between friction and adhesion in coupled mechanical systems.