This paper presents the results of temporal measurements of the soft X-ray radiation intensity in the spectral range of 10–40 eV emitted from the capillary plasma under discharge with a current pulse of 26 kA amplitude and rising rate of about <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$10^12 hboxA/s$</tex> . The experiments were carried out on a pulsed-power facility SIGNAL with ceramic capillaries of 0.3 cm inner diameter and 15.7 cm length, which are filled with argon up to pressures in the range of 0.25–0.5 torr. To interpret the experimental results, a sequence of numerical calculations simulating gas dynamics and level-by-level ionic kinetics of argon plasma was used. The effect of X-ray lasing in the Ne-like line was found to be generated with a quanta energy of 26.4 eV, which lasted for approximately 1–2 ns, at a moment of about 33 ns after the current pulse start.