In this paper, we propose a new and generic methodology for the analysis of texture anisotropy. The methodology is based on the stochastic modeling of textures by anisotropic fractional Brownian fields. It includes original statistical tests that permit to determine whether a texture is anisotropic or not. These tests are based on the estimation of directional parameters of the fields by generalized quadratic variations. Their construction is founded on a new theoretical result about the convergence of test statistics, which is proved in the paper. The methodology is applied to simulated data and discussed. We show that on a database composed of 116 full-field digital mammograms, about 60 percent of textures can be considered as anisotropic with a high level of confidence. These empirical results strongly suggest that anisotropic fractional Brownian fields are better-suited than the commonly used fractional Brownian fields to the modeling of mammogram textures.