Compression‐annealed pyrolytic graphite and single‐crystal graphite specimens were irradiated with neutrons for total exposures of 3 to 71×1017neutrons/cm2(nvt) at 50°C, 3 to 8×1019nvt at 650°C and 1.2×1020nvt at 1000°C. The elastic constants of the materials were determined before and after irradiation by ultrasonic‐, sonic‐resonance‐, and static‐test methods. The only elastic constant that changed significantly with irradiation was the shear modulusc44although a small change was also seen inc33. The natural crystals after irradiation had shear moduli in the range of 0.16–0.46×1011dyn/cm2, the modulus after irradiation showing no correlation with irradiation temperature, exposure, or modulus before irradiation. The average values of the shear modulus of the pyrolytic graphite were 0.22−0.40×1011dyn/cm2after irradiation at 50°C, 0.030−0.033×1011dyn/cm2after irradiation at 650°C, and 0.042×1011dyn/cm2after irradiation at 1000°C; the shear modulusc44of graphite when all dislocations are pinned is thus equal to or greater than 0.40×1011dyn/cm2. The results can be correlated with electron‐microscope observations and interpreted in terms of nucleation theory of radiation damage in analogy to the interpretation of the electron‐microscope observations of W. N. Reynolds and P. A. Thrower [Phil. Mag. 12, 573 (1965)] or in terms of a difference in the availability of sinks for the displaced atoms.