Using a perturbational-analysis and Fourier-transform techniques, we solve the Kukhtarev equations to analyze the steady-state and the transient beam fanning in a photorefractive material. Steady-state results are calculated with both thin- and thick-sample models for the photorefractive material, and the results are compared. The thin-sample results are corroborated with a simple physical argument based on an Airy function approach. We find the nature of the dependence of beam fanning on the beam size and sample thickness. Furthermore, we calculate the transient buildup of beam fanning using the thick-sample model.