High-entropy alloys (HEAs) consisting of multiprincipal elements have demonstrated many interesting structural, physical, and chemical properties for a wide range of applications. This article is a review of the current theoretical research on the elastic parameters of HEAs. The performance of various ab initio-based computational models (effective medium and supercell approaches) is carefully analyzed. Representative theoretical elastic parameters of different HEAs, including single-crystal elastic constants, polycrystalline elastic moduli, elastic anisotropy, and Debye temperature, are presented and discussed. For comparison, simple mixtures of the elastic moduli of pure elements are calculated and contrasted with the ab initio results. The present work provides a reference for future theoretical investigation of the micromechanical properties of systems based on HEAs.