  In 1957 Atiyah classified simple and indecomposable vector bundles on an
elliptic curve. In this article we generalize his classification by describing
the simple vector bundles on all reduced plane cubic curves. Our main result
states that a simple vector bundle on such a curve is completely determined by
its rank, multidegree and determinant. Our approach, based on the
representation theory of boxes, also yields an explicit description of the
corresponding universal families of simple vector bundles.
