Upon cooling typical Pb-alloy Josephson junction devices from 300 to 4.2 K, strain is introduced into the junction electrode films due to the thermal expansion coefficient mismatch between the films and their underlying Si substrates. To reduce the probability of device failure, it is desirable for the strain to be supported elastically by the electrodes. Studies were undertaken by transmission electron microscopy and x-ray diffraction to correlate film microstructure with the elastic strain that can be supported at 4.2 K by Pb-alloy films containing Au and/or In. Grain size was confirmed to be one of the key factors that control the level of the elastic strain supported at 4.2 K when the films contained no misfit dislocations. The critical grain size (g c) (the value larger than which strain relaxation occurs upon cooling to 4.2 K) was found to be ∼0.6 μm for the Pb and Pb-alloy films prepared at 298 K by nucleating them on an ultrathin Au or oxidized In layer in a vacuum lower than 1×10-7 Torr. The Pb-alloy films prepared at 77 K supported more strain elastically; no strain relaxation was observed when their grain sizes were about a factor of two larger than the gc. When films contained misfit dislocations as observed at Pb/In interfaces in Pb-In and Pb-In-Au alloy films prepared at 298 K, strain relaxation by the dislocation glide was observed even though the average grain sizes were smaller than g c. No evidence was obtained that Pb3Au and AuIn 2 intermetallic compounds observed in Pb-Au and Pb-In-Au films, respectively, control the level of elastic strain they can support at 4.2 K. However, these compounds were found to retard grain growth of the Pb-alloy films and to improve their grain size uniformity.