Diffractions play an important role in seismic processing because they can be used for high-resolution imaging and the analysis of subsurface properties like the velocity distribution. Until now, however, only isotropic media have been considered in diffraction imaging. We have developed a method wherein we derive an approximation for the diffraction response for a general 2D anisotropic medium. Our traveltime expression is formulated as a double-square-root equation that allows us to accurately and reliably describe diffraction traveltimes. The diffraction response depends on the ray velocity, which varies with angle and thus offset. To eliminate the angle dependency, we expand the ray velocity in a Taylor series around a reference ray. We choose the fastest ray of the diffraction response, i.e., the ray corresponding to the diffraction apex as the reference ray. Moreover, in an anisotropic medium, the location of the diffraction apex may be shifted with respect to the surface projection of the diffractor location. To properly approximate the diffraction response, we consider this shift. The proposed approximation depends on four independent parameters: the emergence angle of the fastest ray, the ray velocity along this ray, and the first- and second-order derivatives of the ray velocity with respect to the ray angle. These attributes can be determined from the data by a coherence analysis. For the special case of homogeneous media with polar anisotropy, we establish relations between anisotropy parameters and the parameters of the diffraction operator. Therefore, the stacking attributes of the new diffraction operator are suitable to determine anisotropy parameters from the data. Moreover, because diffractions provide a better illumination than reflections, they are particularly suited to analyze seismic anisotropy at the near offsets.