The finite element method is a popular method in numerically solving differential equations  arising from engineering and mathematical modeling. Sheaf theory, on the other hand, is a tool for systematically tracking local data. It is widely used in algebraic geometry and differential geometry. In this talk, I am going to propose a sheaf theory framework for finite elements. This idea works successfully in figuring out conditions for constructing C^r elelment spaces. This provides an envidence that sheaf theory is a suitable framework for finite elements, which are constructed using local data. This talk is base on an on-going joint work with Jun Hu, Ting Lin and Qingyu Wu.