One statistical model that is widely used for propagation prediction in mobile radio systems is the Walfisch model. The Walfisch model is applicable in built-up areas, and uses theoretical methods to relate the mean building height and density to the average path loss. In this dissertation, the Walfisch model is extended for application to fixed wireless access systems. The main extension is to allow for the higher receiver (subscriber) antenna heights that are used in fixed wireless access systems. In addition, allowance is made for the fact that the subscriber antenna typically has highly directional radiation characteristics. A new expression is developed for simulating the field strength of a cylindrical wave as it undergoes multiple diffraction past a series of absorbing half-screens. This also includes a method for minimising the effects of any numerical roundoff errors on the simulation results, and the derivation of an expression for the truncation height of the field in the aperture of each half-screen. This simulation technique is used to evaluate the path loss of the extended Walfisch model for a wide range of built-up environments and subscriber antenna heights, and approximating expressions are fitted to the numerical results. The effects of variations in building height on the model predictions are investigated, under the assumption that building heights are uniformly distributed. New expressions for the average path loss as a function of the standard deviation of building height are also developed, thereby further extending the Walfisch model. The models developed are compared to measurements taken in a suburban area. The measurements were taken at two different frequencies and four different subscriber antenna heights. Good agreement is observed between the theoretical expressions developed and the measurement results when the variation in building height is accounted for.