Research object: composite centrally-compressed structures with semi-rigid nonlinearly deformable connections, which are put into operation at the very beginning of loading the element. Research goal: development of a numerical method for calculating the strength and stability of compressed composite rods, which takes into account the nonlinear deformation of shear bonds, the shear stiffness coefficient of which has the form of a functional dependence and is equal to the angle of inclination of the tangent drawn to the experimental load–strain curve (T–δ) at the point with a given shear force T. Methods: the method of solving the problem consists in dividing the component element into separate sections, compiling a system of equations describing the increment of contiguous fibers in the shear seams. The load is applied in steps, after the next step the total shear forces in the bonds are determined and the stiffness coefficients for the next calculation step are clarified; at each step, the system is “probing” for the possibility of loss of stability. The resulting value of the critical force is compared with the sum of all load steps applied at this stage of the calculation, the calculation stops when the specified calculation accuracy is reached. If necessary, to obtain the resulting values, the received forces in the bonds and the normal stresses in the branches of the component structure are summed up. Results: the calculation of a three-layer timber pillar is presented. The pillar is reinforced with side overlays fastened using nonlinear-compliant shear bonds. The results of linear and nonlinear calculations are compared for different values of the stiffness coefficient of the bonds. The possible calculation error with the normative value of the stiffness coefficient is established.