2000 Mathematics Subject Classification: 53C42, 53C15. In this article, we have studied warped product semi-invariant submanifolds in a locally Riemannian product manifold and introduced the notions of a warped product semi-invariant submanifold. We have also proved several fundamental properties of a warped product semi-invariant in a locally Riemannian product manifold. Supported by the Scientific Research Fund of St. Kl. Ohridski Sofia University under contract 90/2008.