Deep hole technique can be used to drill hole with high depth-diameter-ratio. The propose of the study is investigated the shaft behavior of BTA (Boring and Trapanning Association) deep hole drilling under lateral vibration control with minimum quantity lubrication. The lateral vibration is controlled by magneto-rheological damper. The study is based on theories of pipes conveying fluid with a velocity and Bernoulli-Eulerian theory. The eigenvalues of the shaft effected by fluid flow and damper is investigated.