Measurements are reported of the temperature dependence of the elastic constants, ultrasonic attenuation and thermal expansion of dilute Cr - Ir alloy single crystals containing 0.07, 0.17, 0.20 and 0.25 at.% Ir. Well defined magnetic anomalies were observed in the elastic constants and in the thermal expansion at the Néel points and at the incommensurate - commensurate (I - C) spin-density-wave (SDW) transition temperatures . The transition at , observed in Cr + 0.20 at.% Ir and Cr + 0.25 at.% Ir, is hysteretic, of hysteresis width about 20 K. Magnetic anomalies were also observed in the elastic constants at the spin-flip transition temperature , The attenuation coefficient shows a large spike-like peak at (on heating) and at (on cooling) for Cr + 0.20 at.% Ir. These peaks are however smeared out by inhomogeneities in the crystal containing 0.25 at.% Ir. The attenuation coefficient peaks at and in Cr + 0.07 at.% Ir and in Cr + 0.17 at.% Ir. Due to very large attenuation and the high value of could not be measured successfully around the Néel point for the other crystals. The magnetovolume and magnetic contributions to the bulk modulus (B) have been found to fit the equation , predicted by theory, rather well up to temperatures (T) close to . The volume derivative of calculated from and for Cr + 0.07 at.% Ir, compares fairly well with the value obtained from high-pressure measurements. High-pressure measurements are not available for the other crystals for a similar comparison. The temperature dependence of for Cr + 0.17 at.% Ir fits the power law , predicted by theory for T just above , rather well. The theory however fails in the case of Cr + 0.07 at.% Ir and could not be tested for the other two crystals.