This paper presents applications of the adaptive FEM in computational biomechanics. The study involves finite deformation of artery walls built of layers of elastic, nearly incompressible (rubber-like) materials. The models are reinforced with nearly inextensible collagen fibres stretched along the directions close to the circumferential direction. A Total Lagrangian technique based on the displacement-pressure formulation is presented. Residual error estimates and finite element mesh adaptation strategies are developed. The procedures are illustrated for solutions of arteries under various load considerations.