We investigate the potential of Convolutional Neural Networks (CNNs) for analyzing the regularity in general textures. Regular textures are frequently found in man-made environment, and some biological and physical images. There is a wide range of applications for recognizing and locating regular textures. In this work, we aim to apply CNNs as a general method for classifying regular and irregular textures. We created a new regular texture database and evaluated texture-optimized CNN models and standard CNN models. Our experiments show that the state-of-the-art of standard CNNs attained sufficient accuracy for regular texture recognition tasks. The regular database and code are provided here.