Organic dyes commonly used for planar laser-induced fluorescence (PLIF) are susceptible to photobleaching under laser excitation. Previous work has shown that photobleaching can induce significant errors in laser-induced fluorescence measurements made with single-point techniques. This paper presents an analytical model and experimental results that quantify the extent of photobleaching in the more common planar configuration of the technique. Experimental results for two common dyes, fluorescein and Rhodamine 6G, agree well with analytical predictions for typical PLIF parameters. Results indicate that even dyes such as fluorescein that have large photobleaching constants can be used with little error in many PLIF experiments.