We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold σ , we associate an integer-valued function, called degree , measuring the extent to which σ fails to be cylindrical. In particular, we show that if the degree is constant and equal to d , then the singularities of σ can only occur along an ( m - d ) -dimensional "striction" submanifold. This result allows us to extend the standard classification of developable surfaces in R 3 to the whole family of flat and ruled submanifolds without planar points, also known as rank-one : an open and dense subset of every rank-one submanifold is the union of cylindrical , conical , and tangent regions.