It has recently been demonstrated that black hole dynamics can be reformulated as the equations of motion of a co-dimension one membrane. We generalize this membrane paradigm equations to finite D. This membrane equation comes from conservation of a stress tensor. We also find a simple membrane action whose extremization generates all stationary membrane configurations and consistent with thermodynamics, onshell , which is dual to black hole thermodynamics.  In long wave length limit of this membrane in AdS space the boundary shadow of this membrane dynamics is boundary hydrodynamics. The shadow dual boundary stress tensor reproduces fluid gravity upto first order.