The time spent in drilling ahead is usually a significant portion of total well cost. Drilling is an expensive operation including the cost of equipment and material used during the penetration of rock plus crew efforts in order to finish the well without serious problems. Knowing the rate of penetration should help in speculation of the cost and lead to optimize drilling outgoings. Ten wells in the Nasiriya oil field have been selected based on the availability of the data. Dynamic elastic properties of Mishrif formation in the selected wells were determined by using Interactive Petrophysics (IP V3.5) software based on the las files and log record provided. The average rate of penetration and average dynamic elastic properties for the studied wells was determined and listed with depth. Laboratory measurements were conducted on core samples selected from two wells from the studied wells. Ultrasonic device was used to measure the transit time of compressional and shear waves and to compare these results with log records. The reason behind that is to check the accuracy of the Greenberg-Castagna equation that was used to estimate the shear wave in order to calculate dynamic elastic properties. The model was built using Artificial Neural Network (ANN) to predict the rate of penetration in Mishrif formation in the Nasiriya oil field for the selected wells. The results obtained from the model were compared with the provided rate of penetration from the field and the Mean Square Error (MSE) of the model was 3.58 *10-5.