Material reflectance properties play a central role in photorealistic rendering. Bidirectional texture functions (BTFs) can faithfully represent these complex properties, but their inherent high dimensionality (texture coordinates, color channels, view and illumination spatial directions) requires many coefficients to encode. Numerous algorithms based on tensor decomposition have been proposed for efficient compression of multidimensional BTF arrays, however, these prior methods still grow exponentially in size with the number of dimensions. We tackle the BTF compression problem with a different model, the tensor train (TT) decomposition. The main difference is that TT compression scales linearly with the input dimensionality and is thus much better suited for high-dimensional data tensors. Furthermore, it allows faster random-access texel reconstruction than the previous Tucker-based approaches. We demonstrate the performance benefits of the TT decomposition in terms of accuracy and visual appearance, compression rate and reconstruction speed.