Abstract Methods for simulating the mechanics of debonding and predicting global load-slip (P-Δ) response from local bond stress versus slip (τ-δ) relationships can vary significantly in their complexity. It is generally accepted that an adequate representation of intermediate crack debonding can be achieved by considering only mode-II (shear) fracture along the interfacial bond, a problem that can be solved by accounting for one-dimensional fields of elastic stress and strain in the substrate and plate, and nonlinear interfacial slip and shear stress along the bond. In this paper, full-slip-range analytical solutions are presented for the bilinear τ-δ rule with allowance for residual friction. The procedure is capable of modelling the entire debonding process over both long and short bonded lengths. This is an extension of previous works which are either inapplicable to all bonded lengths or do not allow for residual strength. Applicability of the formulation can range from externally-bonded or near-surface-mounted FRP plates, to embedded bars or bolts in brittle substrates such as concrete, rock or masonry. The versatility and low computational effort required to apply the developed formulation makes it ideal for both directly predicting the P-Δ relationship from known τ-δ parameters, or conversely for extracting a τ-δ relationship from a reference P-Δ curve using inverse calibration. While it is not the purpose of this paper to propose a bond model for any specific type of system, a framework is proposed for doing so. Significantly this framework addresses the difficulty in identifying a unique solution of local properties from experimental data, and highlights that the bonded length has an important influence on the reliability of extracted results.