Using own-design automated pulse equipment at frequencies of 10—30 MHz, the bulk-wave velocities of ultrasonic (US) in the different geometric directions and on various sections of specimens made of archival fragment of the VVER-440 vessel wall (15CrMFA and 08Cr18N10T steels) and 15Cr2NMFA RPV (Reactor Power Vessel) steel of the VVER-1000 vessel as well as density ($\rho$) of the specimens are measured. Using the values of $v_{ij}$ and $\rho$, the acoustic and elastic anisotropy of the alloys and their homogeneity are studied, and the texture US analysis of the two layers of the wall cladding of the VVER-440 vessel is executed. In contrast to the specimens of RPV steels of both reactors, in the cladding of 08Cr18N10T steel, the acoustic and elastic inhomogeneity, anisotropy of US velocities (up to 26%), and corresponding elastic moduli (up to 52%) caused by the presence of clearly determined inhomogeneous texture close to axial one are ascertained. By the temperature dependence of US longitudinal velocity $v_{l}(T)$ in the specimens of the wall components of the VVER-440 vessel, dependences of elastic modules $E$, $G$ and $B$ on $T$ are determined in overall temperature range of 0—300°C for a direction normal to the wall surface. The $v_{l}(T)$ and $E(T)$ dependences were used in previous studies as calibration data. As noted, most of the results are published for the first time, and they must be taken into account in the analysis of the mechanical properties of the VVER vessels and for using in methods of nondestructive ultrasonic testing.