In order to study shear-slip constitutive model of screw connections between cold-formed steel (CFS) profiles and its application in numerical analysis of CFS built-up columns, a total of 225 steel-to-steel screw-fastened connections were investigated under monotonic loads. The thicknesses of C-section steels and diameters of self-drilling screws were varied to study their effect on shear performance of connections. The experimental results show that the failure modes can be divided into three types, which include bearing failure of screw holes, shear failure of screws and pull-out of screws. Furthermore, the shear-slip constitutive model of screw-fastened connections was developed and then the methods for estimating stiffness parameters, strength parameters and displacement parameters were derived. In addition, the numerical models were put forward by applying the shear-slip constitutive model on basis of previous built-up back-to-back CFS columns tests. The results of numerical simulation are consistent with the previous test results by comparisons. The proposed shear-slip constitutive model can effectively simulate the shear-slip behavior of screws used in built-up back-to-back CFS columns. •Monotonic loading tests of steel-to-steel screw-fastened connections were carried out.•Bearing failure of screw holes, shear failure of screws and pull-out of screws are the three types of failure modes.•A shear-slip constitutive model of screw connections was developed.•A numerical model applying the model was developed to simulate built-up back-to-back CFS columns.