Abstract: This paper regards the fluid micro-element as a special case of solid micro-element and considers the nature of no shear stress when the fluid is at rest, the concept of hydrostatic pressure is obtained by using the Cauchy formula of elasticity, then, the equilibrium differential equation of elasticity is used to derive the Euler equation of hydrostatics. By considering the similarities and differences between elastic solid and incompressible viscous fluid, the basic equation of elasticity is used to directly derive the N–S equations for incompressible viscous fluid in fluid dynamics. This method avoids the traditional derivation method of the basic equations of fluid mechanics and proves that the basic equations of elasticity and fluid mechanics are highly unified. The research results can further improve the teaching content of mechanics course, promote the deep understanding of the basic principles of mechanics, and effectively improve the teaching quality of mechanics course.