Friction testing of microfibre arrays is typically conducted under displacement boundary conditions. For example, after the application of a compressive preload, the translation stage is fixed in the vertical direction while a shear displacement is applied by translating the stage laterally. A nonlinear rod model is used to compute the normal and shear forces acting on a typical microfibre during such a test. The normal load acting on a typical fibre is found to switch from compression to tension as the shear displacement increases. The critical shear force to detach a fibre is found to depend linearly on the compressive preload. The fibre is also found to become more stable as it is sheared, hence it never buckles. On the other hand, instead of fixing the vertical displacement, when a fibre is subjected to constant normal load, it becomes unstable upon shearing. We show that the buckling load (the applied normal load to make a fibre unstable) of a microfibril is reduced by the application of a shear displacement.