In the recent years the finite element method was used to determine the contact pressure distribution between any twoelastic bodies, however the effect of friction at the mating surfaces are ignored and no manageable solution for the behaviour of an axi-symmetrical hollow components of finite length has been available. In the present work, the authors consider the problem of fitted tubes with different thickness to diameter ratio and length. The finite element method is used to determine the stress in-tensity-double value of that determined by the maximum shear stress theory. Computed results showed that the stress intensity across tube thickness and along its length is greatly affected by the tube. thickness to diameter ratio, t/di, and tends to approach a constant value for t/di ≥ 0.05. The length ratio between outer and inner tubes, L/L1 , have also a pronounced effect. The stress values on the inner tube increases with the increase in length ratio, while on the outer tube it decreases with the increase in length ratio and tends to have a constant value for L/L1 ≥ 3. Comparing stress intensity results with that evaluated for the hoop stresses showed a slight difference on tube thickness and length, with a maximum difference of 10%.