Converging shock waves in liquids can be used efficiently in the research of the extreme state of matter and in various applications. In this paper, the recent results related to the interaction of a shock wave with plasma preliminarily formed in the vicinity of the shock wave convergence are presented. The shock wave is produced by the underwater electrical explosion of a spherical wire array. The plasma is generated prior to the shock wave's arrival by a low-pressure gas discharge inside a quartz capillary placed at the equatorial plane of the array. Analysis of the Stark broadening of Hα and Hβ spectral lines and line-to-continuum ratio, combined with the ratio of the relative intensities of carbon C III/C II and silicon Si III/Si II lines, were used to determine the plasma density and temperature evolution. It was found that during the first ∼200 ns with respect to the beginning of the plasma compression by the shock wave and when the spectral lines are resolved, the plasma density increases from 2 × 1017 cm−3 to 5 × 1017 cm−3, while the temperature remains at the same value of 3–4 eV. Further, following the model of an adiabatically imploding capillary, the plasma density increases >1019 cm−3, leading to the continuum spectra obtained experimentally, and the plasma temperature >30 eV at radii of compression of ≤20 μm. The data obtained indicate that the shock wave generated by the underwater electrical explosion of a spherical wire array retains its uniformity during the main part of its convergence.