The performance of ten density functional theory (DFT) methods in a prediction of the structure of four clay minerals, in which non-bonding interactions dominate in the layer stacking (dispersive forces in talc and pyrophyllite, and hydrogen bonds in lizardite and kaolinite), is reported. In a set of DFT methods following functionals were included: standard local and semi-local (LDA, PW91, PBE, and RPBE), dispersion corrected (PW91-D2, PBE-D2, RPBE-D2, and vdW-TS), and functionals developed specifically for solids and solid surfaces (PBEsol and AM05). We have shown that the standard DFT functionals fail in the correct prediction of the structural parameters, for which non-bonding interactions are important. The remarkable improvement leading to very good agreement with experimental structures is achieved if the dispersion corrections are included in the DFT calculations. In such cases the relative error for the most sensitive lattice vector c dropped below 1%. Very good performance was also observed for both DFT functionals developed for solids. Especially, the results achieved with the PBEsol are qualitatively similar to those with DFT-D2.