An elastic damage model for concrete has been proposed considering damage-induced bimodularity. A scalar damage parameter has been chosen to quantify the damage. Expressions for the material compliance tensor components have been derived from the assumed strain and complementary energy functions stated in terms of the principal stresses and strains. Incremental constitutive equations have been derived incorporating the elastic behavior due to stress increments as well as stiffness degradation. Within the current damage surface, the stiffness of the material with constant damage varies with applied stress variations. During loading beyond the current damage surface, the material experiences stiffness degradation due to increase in extent of damage suffered by it. Using the proposed elastic damage model, the material response has been predicted for different load histories.