In this paper, we study static bending and free vibration behavior of Bernoulli–Euler micro-beams with a single delamination using the modified couple stress theory. The delaminated beam is modeled by four interconnected sub-beams using the delamination zone as their boundaries. The free and constrained mode theories have been utilized to model the interaction of delamination surfaces in the damaged area. The continuity as well as compatibility conditions are satisfied between the neighboring sub-beams. After verification of the results for some case studies with available solutions, the effect of various parameters such as spanwise and thicknesswise locations of the delamination, material length scale parameter, and boundary conditions on the static bending and free vibration characteristics of the size-dependent micro-beam have been investigated in detail.