In this paper, we address the relatively unexplored problem of classifying texture surfaces undergoing significant levels of non-rigid deformation. State-of-the-art texture classification methods have demonstrated to be very effective for classifying fronto-parallel texture fields. Recently, affine-invariant descriptors have been proposed as an effective way to model local perspective distortion in textures. However, if the effects of local surface curvature distortion are large, affine-invariant descriptors become unreliable. Our contribution in this paper is twofold. First, we propose a method for learning representative basic elements of non-fronto-parallel texture fields undergoing non-rigid deformations. Secondly, we demonstrate the effectiveness of our texture learning method for the classification of non-rigid deforming texture surfaces. We test our method on a set of images obtained from man-made texture surfaces.