This paper introduces a novel and user-friendly analytical approach for modeling the debonding phenomenon in steel reinforced grout (SRG) strengthened concrete specimens subjected to single lap shear tests. Nonlinearity is localized at the interface between substrate and reinforcement assumed to be linear elastic. The behavior at this interface, supposed to be discontinuous and multilinear, is defined by a tangential stress-slip relationship comprising four phases: three elastics perfectly fragile and one elastic perfectly ductile. An observed pseudo-linear hardening phase is evident in experiments in force-displacement curves upon detachment initiation, underscoring the necessity of considering a non-zero residual tangential resistance at the interface. With these assumptions in place, the slip at the interface between reinforcement and substrate can be characterized by a second-order differential equation that yields closed-form solutions upon proper derivation. Additionally, this paper proposes an implementation into a commercial finite element (FE) software, wherein the interface between substrate and reinforcement is discretized using three cutoff bars in parallel, two of which are elastic perfectly fragile and one elastic perfectly ductile, employing rigid beams for connections and modeling SRG with elastic quadrilateral elements. Ultimately, the reliability of the proposed analytical and numerical methodology is confirmed through validation against experimental tests available in the literature for which five SRG-strengthened specimens subjected to direct shear tests are used.