The thin films of titanium nitride (TiN) with the thickness of 0.5, 1.0, 2.0, 4.0 mum were coated on a steel substrate by the ion beam mixing method. The film had a strong fiber texture with <110> axis perpendicular to the film surface. The initial residual stress was equi-biaxial compression between -4.4 to -5.6 GPa. For all thickness cases, the initial part of the changes of the in-plane stresses in the film due to external tensile loading agreed well with the prediction based on elasticity. While the substrate was under a uniaxial stress, the film was in the biaxial state of stress because of the mismatch of Poisson's ratio. When the measured stress in the film exceeded a certain value, the stress departed from the linear relation and leveled off. The onset of nonlinearity was nearly coincident with the first appearance of cracks. The stresses at the onset of nonlinearity and leveling-off decreased with increasing film thickness.