In this talk we analyse the behavior of the solutions of linear elliptic equations posed in a two dimensional domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine linear homogenization theory for reticulated structures and variational methods to obtain the limit problem and convergence results as well. This is a joint work with: J. M. Arrieta (UCM - Madrid/Spain), A. N. Carvalho (USP - Sao Carlos/Brazil) and M. C. Pereira (USP - Sao Paulo/Brazil).