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Secondary grain growth in thin films can lead to grain sizes much greater than the film thickness. Surface energy anisotropy often provides an important fraction of the driving force for secondary grain growth, especially in the early stages of growth. Surface‐energy‐driven secondary grain growth leads to the development of large grains with restricted crystallographic textures. A model is presented for growth of secondary grains into a uniform matrix of columnar normal grains. The model indicates that secondary grain growth rates should increase with grain boundary energy, surface energy anisotropy, grain boundary mobility, and temperature. While final secondary grain sizes will decrease with film thickness, their growth rates will increase. The final secondary grain sizes and orientations will be strongly affected by grain sizes and orientations in the initial film. The models presented here provide analytical tools for experimental study of secondary grain growth in thin films. They will be used in forthcoming publications describing experimental study of secondary grain growth in silicon and germanium.