To interpret H2 quasar absorption line observations in DLAs (damped Lyα clouds), we model the H2 spatial distribution within a DLA. Based on numerical simulations of disk structures with parameters similar to those derived for such absorbers, we calculate the H2 distribution as a function of ultraviolet background (UVB) intensity and dust-to-gas ratio. For typical values of these two quantities we find that the area in which the H2 fraction exceeds 10−6 (typical observational detection limit) only covers < 10% of the disk surface, i.e., H2 has a very inhomogeneous, clumpy distribution even at these low abundance levels. This explains the relative paucity of H2 detections in DLAs. We also show the dependence of the covering fraction of H2 on dust-to-gas ratio and UVB intensity and we comment on the physics governing the H2 chemical network at high redshift. We finally comment on our implication on the statistics of the H2 column density distribution.