The growth kinetics of Ni3Al were investigated in Ni//NiAl macroscopic diffusion couples annealed at 800–1000 °C under applied elastic compressive stress. By utilizing electron backscatter diffraction (EBSD) technology in conjunction with appropriate statistical methods, the mechanism underlying the impact of elastic stress on Ni3Al growth kinetics is elucidated. Based on the findings, the application of compressive elastic stress can enhance Ni3Al growth kinetics by increasing both atomic vibration frequency (ν) and activation entropy (Δs). The newly formed Ni3Al phase at the Ni/NiAl interface exhibits a specific crystallographic relationship with adjacent NiAl phase, with most Ni3Al grains maintaining a Kurdjumov-Sachs (KS) orientation relationship. Remarkably, the application of elastic compressive stress in conjunction with an increase in temperature results in a reduction of Ni3Al grains grown according to the KS orientation relationship.