Well stimulation using acidic solutions is widely used to treat carbonate formations. The acidic fluids remove the near-wellbore damage and create channels around the wellbore by dissolving fraction of the carbonate rocks. Many stimulation fluids have been used such as hydrochloric acid (HCl) acid, organic acids, and chelating agents to stimulate carbonate reservoirs. Wormholes that are created by these fluids are very effective and will yield negative skin values and this will enhance the well productivity. In addition to the wormhole creation, the diffusion of these fluids inside the pores of the rock may create significant and permanent changes in the rock mechanical properties. These changes can eventually lead to weakening the rock strength, which may lead to future formation damage due to the wellbore instability. In this paper, the effect of ethylenediaminetetraacetic acid (EDTA) and diethylenetriaminepentaacetic acid (DTPA) chelating agents on the carbonate rocks elastic properties was investigated. The effect of wormholes created by chelating agent on the rock mechanical properties was investigated. Computed tomography (CT) scan and acoustic measurements were conducted on the core samples before and after matrix stimulation treatments. Experimental results showed that the mechanical properties of strong rocks such as Indiana limestone (IL) cores were not affected when chelating agents were used to stimulate those cores. On the other hand, less strong rocks such as Austin chalk (AC) show significant alteration on the rock elastic properties when chelating agents were used as stimulation fluids.