This article briefly reviews the reported elastic parameters of cubic high entropy alloys (HEAs), including single-crystal elastic constants, polycrystalline elastic moduli, Debye temperature, and elastic anisotropy. Modern ab initio calculations prove to be a powerful and accurate approach that complements the experimental study of elastic properties of HEAs. Correlations between current theoretical and experimental elastic parameters (e.g., specific modulus versus Pugh ratio) are investigated. The high degree of variability of elastic behavior of HEAs makes them particularly attractive in designing future structural materials with desired properties.