  An action principle of singular hypersurfaces in general relativity and
scalar-tensor type theories of gravity in the Einstein frame is presented
without assuming any symmetry. The action principle is manifestly doubly
covariant in the sense that coordinate systems on and off a hypersurface are
disentangled and can be independently specified. It is shown that, including
variation of the metric, the position of the hypersurface and matter fields,
the variational principle gives the correct set of equations of motion: the
Einstein equation off the hypersurface, Israel's junction condition in a doubly
covariant form and equations of motion of matter fields including the scalar
fields. The position of the hypersurface measured from one side of the
hypersurface and that measured from another side can be independently variated
as required by the double covariance.
