Volume self-sustained discharges in gases at high pressure are formed with the use of pre-ionization sources and are widely used for pulsed laser pumping [1, 2]. In a pulsed nanosecond discharge [3, 4], the conditions can be realized in which the time of discharge channel formation is less than the voltage pulse duration. Then the volume discharge is formed under conditions of multielectron initiation when the initial voltage exceeds the static breakdown voltage. In [5–9], the volume pulsed discharge was initiated in air and other gases at atmospheric pressure without preionization source. To this end, nanosecond high-voltage pulses (~100 kV and more) with a leading pulse edge duration of ~1 ns and less were applied to the gap in [5–9]. The anode was flat, and the cathode had a small radius of curvature. With increase in the interelectrode gap, a pulse corona discharge was observed under these conditions. The main difference between volume and corona pulsed discharges is that in the corona discharge, the gas is ionized only in a part of the gap with the highest electric field strength. In the volume discharge, the gas is ionized in the entire gap, which allows high current densities on the anode (~3 kA/cm), high specific deposited power (~1 J/cm), and high specific pump power density (~400 MW/cm) to be obtained [6–9]. The diffusion discharge with a brighter central channel was realized in [10] when the voltage pulse duration increased up to 170 ns and the leading edge pulse duration increased up to 10 ns. This means that the discharge constriction is observed with increasing pulse duration. However, in [5–10] much attention was given to the study of the discharge initiated in gaps with the potential cathode having a small radius of curvature, and the influence of voltage pulse polarity and a decrease in the strength of electric field applied to the gap on the formation of the volume discharge was not investigated. Only in [9] the volume discharge was realized in air at atmospheric pressure and near the tip anode (the electrode of a shear discharger). The volume discharges initiated in comparatively short interelectrode gaps or with preionization sources were investigated in [1–4]. The present study investigates the influence of polarity and radius of curvature of the electrodes on the formation of the volume pulsed discharge without pre-ionization source under application of nanosecond voltage pulses of comparatively high amplitude (~100 kV). In our experiments we used the pulse generator of the ARINA x-ray apparatus [4]. The open-circuit gap voltage was about 150 kV and the leading pulse edge duration was less than 1 ns. The voltage pulse polarity could be both positive and negative. The pulse duration at half-maximum was ~2 ns for the volume discharge. Three types of the potential metal electrodes were used, including a sphere 40 mm in diameter (electrode No. 1), a tube 6 mm in diameter fabricated from a foil 50 μm thick (electrode No. 2), and a tip (electrode No. 3). The electrode was connected through a metal rod to a peaking spark-gap of the ARINA apparatus and was placed into a chamber with an inner diameter of 160 mm fabricated from a copper foil. This chamber had a flat bottom used as the second electrode. The interelectrode gap could be increased from 20 to 70 mm. All investigations of the discharge formation were conducted in air at a pressure of 1 atm. During our experiments, the total discharge glow (Fig. 1) was registered together with current and voltage waveforms. As in [5–9], the volume discharge (Fig. 1a) was stably recorded when the voltage pulse of negative polarity was applied to the electrodes with a small radius of curvature (Nos. 2 and 3). Bright spots are seen only on the cathode; volume plasma jets started from these spots. In [6] the discharge of this type was called VADIEB (volume avalanche discharge