It has been shown by model building studies that various right handed and left handed models are compatible with X-ray data of B-DNA and C-DNA. These models are also found to be in good agreement with infrared dichroism data. Detailed potential energy calculations have now been carried out for these models, viz., right and left handed B-DNA and right and left handed C-DNA. It is found that base sugar stacking and interactions involving the phosphate groups are the dominant forces for stabilizing a particular structure. For some sequences, viz., A-A, T-A and C-A, left handed stacking is quite favourable in both B and C structures. But intranucleotide interactions make the left B-DNA unfavourable while the left C-DNA structure is more stable, for all the sequences, than the right C-DNA structure, proposed from fibre data. For the hexanucleoside pentaphosphate fragments the same trend is observed, with the right handed B-DNA being the most stable of the four models studied. However, the left C-DNA structure is only marginally higher in energy, particularly if the shielding effect of the counter ions, on the phosphate group is taken into consideration.