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. Assuming authorial method and procedure for determining dynamic similarity criteria, its have been presented and analysed in the paper both well known similarity numbers obtained in another way (e.g. from dimensional analysis or differential equations for particular problems – as Reynolds, Froude, Euler, Cauchy, Strouhal, Mach numbers) – as well as several new similarity numbers encountered in different fluid solid interaction problems (e.g. new forces and moments coefficients encountered in problems of vibrating solid bodies in fluids).