  A space curve in a Euclidean 3-space $\mathbb E^3$ is called a rectifying
curve if its position vector field always lies in its rectifying plane. This
notion of rectifying curves was introduced by the author in [Amer. Math.
Monthly {\bf 110} (2003), no. 2, 147-152]. In this present article, we
introduce and study the notion of rectifying submanifolds in Euclidean spaces.
In particular, we prove that a Euclidean submanifold is rectifying if and only
if the tangential component of its position vector field is a concurrent vector
field. Moreover, rectifying submanifolds with arbitrary codimension are
completely determined.
