This paper discuss about embedding on the new interconnection network named Torus-Butterfly. Torus-Butterfly is the Cartesian product network that has constant degree and has smaller network cost than the other Cartesian product network. Torus-Butterfly network is a Cayley graph. From the properties of Cayley graphs which have Hamiltonian path, the linear array and 2D-Mesh can be embedded into this new Torus-Butterfly network with minimum dilation and expansion.