The paper presents the results of a numerical investigation of the dynamics of a sliding discharge in a capillary with spatial dimensions similar to those typically used in X-ray sources based on fast capillary discharges. The discharge is created in argon at pressure p = 9 Torr by applying a voltage pulse of negative polarity with an amplitude of 5 kV, a rise time of 5 ns, and a duration of 20 ns. Obtained distributions of main discharge parameters reproduce basic characteristics of a sliding discharge and reveal the mechanism of discharge propagation. The electric field in the front of the discharge is defined by a negative space charge, which at a given moment during discharge propagation is localized in a narrow region along the dielectric surface. For the considered case, discharge propagation is accompanied by full charging of the dielectric surface. The influence of gas pressure on discharge is investigated within range p = 2-25 Torr. Extrema in dependencies of total discharge time and front velocity on gas pressure are obtained in simulations and analyzed.