A two-step critical path analysis (CPA) is combined with effective medium approximation for the development of phenomenological models, correlating the absolute permeability and electrical formation factor of single fractures with structural parameters of their aperture. The functional form of the CPA models is valid not only at the vicinity of percolation threshold but also far from it. The fracture aperture is regarded as a two-dimensional network of elliptical channels with the following parameters: the distributions of the major and minor channel axis lengths, the mean channel length, and the mean coordination number of the network. The models are evaluated with respect to numerical simulations in two-dimensional square lattices and experimental results from artificial glass-etched fractures and are found to be adequate for estimating the transport properties of single fractures for a broad range of parameter values of their aperture. In converse, models based on the conventional CPA, as applied to elliptical channel networks, are unable to predict satisfactorily simulated results.