Using the van der Waals density functionals (vdW-DFs), we present results of a density functional theory (DFT) study on the structure of layered titanium dichalcogenides TiX(2) (X = S, Se, or Te). By accounting for non-local component in long-ranged electron correlation effects, the vdW-DFs lead to more accurate predictions of the structural parameters relative to conventional DFT. In particular, the vdW-optB86b functional [J. Klimeš et al., Phys. Rev. B 83, 195131 (2011)] gives the most agreement with experimental measurements for the lattice constant involving the vdW interactions. Based on the relaxed structure, the calculated elastic constants and vibrational frequencies are compared to experimental work and overall good agreement is obtained.