The 2MFGC catalogue of galaxies selected from the 2MASS catalogue lists over 18000 galaxies with axial ratio no more than 0.33. Thus it is a good object for the application of the anisotropy analysis method proposed by S. L. Parnovsky, I. D. Karachentsev, and V. E. Karachentseva. To estimate statistical significance of the derived anisotropy in distribution of galaxy axes directions we used the Monte-Carlo method. The anisotropy of the whole catalogue is insignificant but the anisotropy of many subsamples is statistically significant up to 99 % level. We analysed a possible nature of this anisotropy to determine whether it is real or induced by selection and measurement errors.