Vegetation stripes ("tiger bush") are a characteristic feature of semi-arid environments. The stripes typically lie along the contours of gentle slopes, and some authors report a gradual uphill migration. A previous mathematical model (Klausmeier, Science, 284:1826, 1999) has shown that this phenomenon can be explained relatively simply by the downhill flow of rainwater coupled with the diffusive spread of the plant population. This paper presents a detailed analysis of pattern formation in the Klausmeier model. The author derives formulae for the wavelength and migration speed of the predicted patterns, and systematically investigates how these depend on model parameters. The results make new predictions and suggest possible approaches to testing the model. © Springer-Verlag 2005.