Because line‐patterned &egr;‐phase Pb‐Bi films are used as the counterelectrode materials of Pb‐alloy Josephson junction integrated circuits presently under investigation, a study was undertaken on the effects of the film width on the strain distribution and average elastic strain supported by the film at 4.2 K. The study was carried out using an x‐ray diffraction technique for 0.6‐&mgr;m‐thick Pb‐29% Bi films that were deposited onto oxidized Si wafers at 273 K, and then cooled to 4.2 K. The blanket films supported almost all of the strain elastically at 4.2 K, and symmetric x‐ray diffraction peak profiles were observed in the films, indicating that they were uniformly strained. Asymmetric peak profiles due to nonuniform strain distributions in the film were observed when the film width was smaller than ∼40 &mgr;m. The measured x‐ray diffraction peak profiles were analyzed using a computer simulation technique. The analysis indicated that the strain distribution at the center of the film is close to the one calculated using the energy minimization method developed by Aleck. Average strains supported elastically at 4.2 K by the films were observed to decrease with decreasing the film widths as predicted by the model, and excellent agreement was obtained between the measured and calculated average strains in the films with various film widths. However, the high local strain at the film edges predicted by this model is not observed. The strain is believed to relax during cooling to 4.2 K.