A computational model is introduced which employs transformation-based media to increase the computational performance of finite methods (such as finite element or finite difference methods) for analyzing waveguides with grooves or rough surfaces. Random behavior of the roughness is taken into account by utilizing the Monte Carlo technique, which is based on a set of random rough surfaces generated from Gaussian distribution. The main objective of the proposed approach is to create a single mesh, and to analyze the effects of the parameters of grooves (such as shape and height) and of roughness (correlation length and root-mean-square height) on both transverse magnetic and transverse electric mode cutoff wavenumbers and field distributions, without repeating mesh generation at each step. This is achieved by introducing a transformation medium within the computational domain, and by computing the material parameters of the medium via the coordinate transformation technique. At each time the surface geometry is changed, only the material parameters are recomputed with respect to the new geometry. Therefore, a great reduction in CPU time is achieved. The technique is analyzed by means of various finite element simulations involving both 2-D parallel plate waveguides and 3-D waveguides of uniform cross section.