To study the relationship between brittleness index and elastic strain energy, the lateral strain response method was used to determine the crack initiation stress of hard rock. By using the crack initiation stress and peak stress of rock, the relationship between brittleness index and elastic strain energy was explained based on fracture mechanics theory and energy theory, and a functional relationships were constructed between brittleness index and elastic strain energy from uniaxial compression test for two types of rock. Results show that the brittleness indexes B₁₃, B₁₄are in power function relationship with the crack initiation elastic strain energy (single variable), and the brittleness indexes B₁₅, B₁₆are in power or linear function relationships with the crack initiation elastic strain energy (single variable). However, no apparent functional relationship was discovered between the brittleness indexes B₁₃, B₁₄, B₁₅, B₁₆and the peak elastic strain energy (single variable). The new brittleness index could be either obtained from both the crack initiation strain energy and the peak elastic strain energy (two variables), or the crack initiation elastic strain energy (single variable). The relationship between brittleness index and the peak elastic strain energy is of great significance for studying rock burst proneness. The calculation method for brittleness index was redefined. Besides, the verifications of two examples show that this method, using the crack initiation elastic strain energy, demonstrates certain credibility. This study provides a new method determining the relationship between brittleness index and the crack initiation elastic strain energy of rock.