In this talk, I would like to discuss the homogenization of the partial differential equations with an oscillating data on a lower dimensional surfaces. Such problems arise on standard Dirichlet or Neumann problems with oscillating boundary data and free boundary problems. The lower dimensional character creates similar issues: oscillating of boundary in mod 1, multiple limits on rational direction and unique behavior on the irrational direction, which will be discussed through examples. And we find out the effective data by some estimates on the so-called correctors which will be used to correct super- or sub-solutions of the homogenized equation to be a super- or sub-solution of є-problems. And then we will discuss the general lower dimensional surface.