A new theoretical calculation method for the load-slip curve and the shear stiffness of the stud based on Winkler’s elastic foundation beam theory and deflection differential equation of the stud is proposed. Different stress characteristics of the elastic and plastic zones of the concrete are considered in the proposed method. The accuracy of the theoretical calculation method is validated by the test results. Moreover, the effect of concrete strength, stud diameter, and yield strength on the stud load-slip curve is analyzed. The results show that the proposed model can effectively reflect the change process of the load-slip curve of the test specimen stud connector. The stud diameter, stud yield strength, and concrete strength affect the peak slip, shear stiffness, and shear capacity of stud shear connectors. With an increase in stud diameter, the peak slip, shear stiffness, and shear bearing capacity of the stud are all increased. An increase in the yield strength of the stud increases its elastic slip, peak slip, and shear capacity. Lastly, with an increase in concrete strength, the elastic slip and peak slip of the stud both decrease, whereas the shear stiffness and shear bearing capacity are increased.