Cy3 and Cy5 cyanine dyes terminally attached to the 5'C end (C1) of the DNA oligonucleotide were studied by metadynamics (MTD), molecular dynamics (MD), and density-functional methods with dispersion corrections (DFT-D). MTD simulations explored the free energy surface (FES) of the dyeDNA interactions, which included stacking and major groove binding motifs and unstacked structures. Dynamics of the stacked structures was studied by the MD simulations. All possible combinations of stacking interactions between the two indole rings of the dyes and the neighbor guanine and cytosine rings were observed. The most probable interaction included the stacking between the dyes distal indole ring and the guanine base. In similar to 10% of the structures the delocalized pi-electrons of the dyes polymethine linkers played a key role in the dyeDNA dispersion interactions. The stacked conformers of the Cy3 dye were confirmed as true minima by DFT-D full optimizations. The stacked dye decreased flexibility up to two neighbor base pairs.