The recent synthesis of the new polymers has been profoundly affected by the unique characteristics of Dimer Acid. These polymers were made up following the condensation with triethanolamine when was treated in melted phase. We performed identification of the physical characteristics of the polymers such as the molecular weight, in addition to the acid value and hydroxyl value. Infrared spectroscopy have been used in identification of this polymer. Also, the rheological behavior has been assessed thermally and shearing stress by using capillary viscometer. Our results revealed a reduction in the viscosity with increase of the shearing stress as will as with rise in the temperature.