The constriction of the positive column of a glow discharge in argon was studied both experimentally and theoretically. In experiments the direct current discharge was maintained in a cylindrical glass tube of 3 cm internal diameter and 75 cm length. The voltage-current U(I) characteristics of the discharge were measured at a gas pressure P from 1 to 120 Torr in a wide range of discharge currents. At P > 20 Torr the measured U(I) characteristics display the classical hysteresis effect: the transition from the diffuse to the contracted discharge form (with increasing current) occurs at a current higher than that for reverse transition (with decreasing current). It was also found that in some cases the so-called partially contracted form of the discharge is realized, when the diffuse and contracted forms coexist in the discharge tube. To calculate the plasma parameters under experimental conditions a 1D axial-symmetric discharge model for pure argon was developed. The details of the model are described and the results of simulations are presented. In particular, the electric field strength E in the positive column was calculated as a function of the discharge current. Theoretical E(I) characteristics are compared with those derived from the experiment. For the first time, the detailed kinetic model without the usage of fit parameters predicts the hysteresis effect in pure Ar with parameters of diffuse and constricted forms of the discharge in good agreement with the experiment.