A generic strictly semistable bundle of degree zero over a curve $$X$$ has a reducible theta divisor, given by the sum of the theta divisors of the stable summands of the associated graded bundle. The converse is not true: Beauville and Raynaud have each constructed stable bundles with reducible theta divisors. For $$X$$ of genus $$g \ge 5$$ , we construct stable vector bundles over $$X$$ of rank $$r$$ for all $$r \ge 5$$ with reducible and nonreduced theta divisors. We also adapt the construction to symplectic bundles. In the “Appendix”, Raynaud’s original example of a stable rank 2 vector bundle with reducible theta divisor over a bi-elliptic curve of genus 3 is generalized to bi-elliptic curves of genus $$g \ge 3$$ .