A computational model is presented for Monte Carlo simulation of waveguides with ridges, by combining the principles of transformation electromagnetics and the finite methods (such as finite element or finite difference methods). The principle idea is to place a transformation medium around the ridge structure, so that a single and easy-to-generate mesh can be used for each realization of the Monte Carlo simulation. Hence, this approach leads to less computational resources. The technique is validated by means of various finite element simulations in the context of 3D waveguides of uniform cross-section. (c) 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.