Living organs, tissues, and cells functionally adapt themselves to mechanical demands, and remodel by changing geometry, structure, and properties. The key factor for this phenomenon is "Mechanical Stress". Major stresses applied to blood vessels inside the body are: (1) hoop stress induced by blood pressure, that is normal stress in the wall circumferential direction, (2) wall shear stress developed by blood flow, and (3) axial stress by elongation in the axial direction. This review article deals with biomechanical studies on the responses of arterial and venous wall to the elevation of blood pressure. One of the specific biomechanical manifestations to arterial wall adaptation in response to hypertension is wall hypertrophy. This restores circumferential wall stress, i.e. hoop stress, at in vivo operating pressure to a normal value, and changes arterial stiffness to an optimal level. Vascular smooth muscle cells are activated by hypertension. Essentially similar phenomena are also observed in venous wall.