  The three-dimensional jump conditions for the pressure and velocity fields,
up to the second normal derivative,across an incompressible/inextensible
interface in the Stokes regime are derived herein. The fluid viscosity is only
piecewise continuous in the domain while the embedded interface exerts singular
forces on the surround fluids. This gives rise to discontinuous solutions in
the pressure and velocity field. These jump conditions are required to develop
accurate numerical methods, such as the Immersed Interface Method, for the
solutions of the Stokes equations in such situations.
