The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. Mxf6;bius cubes form a class of hypercube variants that give better performance with the same number of edges and vertices. In this paper, we consider embedding of meshes in Mxf6;bius cubes. The main results obtained in this paper are: (1) For n≥1, there exists a f16381" title="Click to view the MathML source" alt="Click to view the MathML source">2×2n−1 mesh that can be embedded in the n-dimensional Mxf6;bius cube with dilation 1 and expansion 1. (2) For n≥4, there exists a 4×2n−2 mesh that can be embedded in the f1942a9654" title="Click to view the MathML source" alt="Click to view the MathML source">n-dimensional Mxf6;bius cube with dilation 2 and expansion 1. (3) For n≥4, there are two disjoint 4×2n−3 meshes that can be embedded in the 0-type n-dimensional Mxf6;bius cube with dilation 1. (4) For n≥4, there are two disjoint 4×2n−3 meshes that can be embedded in the 1-type f1555da771" title="Click to view the MathML source" alt="Click to view the MathML source">n-dimensional Mxf6;bius cube with dilation 2. Results of (1) and (3) are optimal in the sense that the dilations of the embeddings are 1.