As vibrations from vortex-shedding occur at moderate wind speeds, structures undergo a considerable number of stress variations. So risk of fatigue is to be taken into account at the design stage itself. Even if a fatigue analysis is not demanded in the code to be applied, risk of fatigue is to be considered, especially with regard to slender steel chimneys due to larger volumes of material subjected to high stresses. Thus, risk of fatigue which has not been addressed in the Indian context, has been taken care in the present paper. It is envisaged that this formulation will be appropriate for inclusion in Indian codes and standards. As part of the case study, a chimney from an industry having Diesel Power Plant has been undertaken. Fatigue analysis of this chimney has been done and measures to reduce fatigue problem have been suggested.