  The Young-Laplace's equation is established based on liquid membrane without
shearing resistance. It is not valid for solid. By taking into account the
in-plane shearing and transverse shearing within the surface layer, we
reconstruct the Young-Laplace's equation so as to characterize the surface of
solid. A new version of the Young-Laplace's equation is proposed. It shows that
the surface equilibrium of solid is determined by the bulk stress, surface
membrane stress and surface transverse stress together. The transverse shear
stress depends on the gradient of the Gaussian curvature of surface and strain.
The intrinsic membrane stress and surface transverse shear stress cause the
residual stresses to appear in the interior of solid. The intrinsic surface
transverse shear stress only occurs in the non-spherical body.
