The crossed cube is an important variant of the hypercube which is the most popular interconnection network for parallel processing. This paper is concerned with the problem of embedding meshes/tori in faulty crossed cubes. We reduce this mesh/tori embedding problem to the problem of embedding paths/cycles in faulty crossed cubes. Then, by exploiting the fault-tolerant pancyclicity of crossed cubes of lower dimension, several schemes for embedding 2D or 3D meshes/tori in faulty crossed cubes are proposed. All of these embeddings have small dilations and small congestions. The obtained results show that the parallel algorithms with mesh/torus task graphs can be efficiently executed on faulty crossed cubes. © 2010 Elsevier B.V. All rights reserved.