The aim of the current  study is to determine the elastic properties  of carbonate rocks using ultrasonic method.  Forty rock samples of  Anah formation  were collected at  different depths from  four wells drilled at the study area . The relationship between wave velocities and elastic properties of rocks was defined. Regression analyses to define these relations were applied. The results indicate that the elastic properties of the rocks show a linear relationship with both P- and S-wave velocities. The best relationship was obtained between both Young's modulus and Shear modulus with Vs in the determination of the coefficient ( R²  ), with values of 0.91 and 0.94,  respectively.  Bulk modulus and  Lame’s constant were  better correlated with Vp than with Vs  in the determination of R²,with values of 0.92 and 0.83, respectively. Poisson’s ratio  showed a good correlation using the ratio of Vp/Vs in the determination of R², with a value of 0.81. The main output of this  study shows that the ultrasonic method is a useful tool for the prediction of the elastic dynamic properties of sample rocks and that it can be used as an economical , simple and  non- destructive method, especially for engineering purposes.