In  June 23, 2006’s “Science” magazine, Pendry et al and Leonhardt independently published their papers on electromagnetic

cloaking. In Nov.10, 2006’s Science magazine, Pendry et al demonstrated the first practical realization of such a cloak with the use of artificially constructed metamaterials. Since then, there is a growing interest in using metamaterials to design invisibility cloaks. In this talk, I will first give a brief introduction to invisibility cloaks with metamaterials, then I will focus on time-domain carpet cloak and arbitray shaped cloaking models.  Well-posedness study and time-domain finite element method for these models will be presented. Numerical simulations of these cloaking phenomena will be demonstrated. I will conclude the talk with some open issues.