Spin valves containing a Dy layer have been formed on an elastic polyimide film by magnetron sputtering. The field dependences of the magnetoresistance of samples subjected to different tensile deformations have been measured. The character of the variations of the magnetoresistive properties of a spin valve subjected to tensile deformation is shown to depend on the thickness of the dysprosium layer. In particular, the thickness of the dysprosium layer affects the maximum relative elongation at which the magnetoresistance of spin valves remains unchanged.