The work concerns dynamic similarity criteria of various phenomena occurring in hydraulics and fluid dynamics originally derived from ratios of forces and forces moments affecting these phenomena. The base of dynamic similarity criteria formulations and considerations is A.Flaga’s method and procedure for determining dynamic similarity criteria in different issues of fluid-solid interactions i.e. at different fluid-solid relative motions. The paper concerns the determination and analysis of dynamic similarity criteria for various practical problems encountered mainly in hydraulics and fluid dynamics at steady, smooth fluid onflow in front of a solid. Moreover, the cases of mechanically induced vibrations of a body in a stationary fluid moving with constant velocity in front of the body have been presented. The paper concerns the determination and analysis of dynamic similarity criteria for various practical problems encountered mainly in hydraulics and fluid dynamics at steady, smooth fluid onflow in front of a solid. Moreover, the cases of mechanically induced vibrations of a body in a stationary fluid moving with constant velocity in front of the body have been presented.