The coordinate transformation technique (with its current name of transformation electromagnetics) is applied to the finite-element method (FEM) with periodic boundary conditions for efficient Monte Carlo simulation of one-dimensional random rough surface scattering problems. In a unit cell of periodic structure, two coordinate transformations are used, one of which is a real transformation designed to model the rough surface with flat surface, and the other is a complex transformation used to design a perfectly matched layer for mesh truncation. The approach is easily implementable because only the nodal coordinates are replaced by the transformed coordinates in a standard FEM. Since a simple and single mesh with flat surface is used, Monte Carlo simulations are performed in an efficient manner. Numerical results are presented for various rms surface heights, correlation lengths, and angles of incidence. (c) 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:322-329, 2016.