A holomorphic isometric embedding is said to be non-standard if the image of the embedding is not totally geodesic. Denote by $H$ the upper half-plane, which is biholomorphically equivalent to the Poincare disk. Denote by $H_p$ the Siegel upper half-plane, which is biholomorphically equivalent to the classical domain of type three. A non-standard holomorphic isometric embedding of $H$ into $H_3$ was constructed by Mok. In this talk, we present non-standard holomorphic isometric embeddings of $H$ into $H_p$ for an arbitrary $p\ge 3$, which include Mok's example as a special case.