Abstarct: The calculation of terrain correction is one of the most important corrections in gravimetry. For many years, this work has been calculated in different ways in geophysical studies. The purpose of this study is to investigate the terrain correction by integrating with various elements such as prism, tesseroid and pointmass, and also to study the corrections of gravimetry, the concept of freeair anomaly and Bouguer anomaly. To calculate the terrain correction Newton's integral with these elements is used. Also using MATLAB programming and then the results of these methods are compared. The constraints and advantages of each various elements are also mentioned. Then, the amount of this effect is calculated by using the Oasis Montaj software. The concept of freeair anomaly from a classic and modern perspective is calculated baxsed on existing relationships and various models for calculating Bouguer anomaly have been investigated. The results indicate that for the calculating of terrain correction three zones are needed such as nearzone, middlezone and farzone. Prism method for nearzone, tesseroid for middlezone and pointmass for farzone are suitable. The concept of frreair anomaly has been calculated from the classic and modern views. Differences in results can be explained by the dirrefences in algorithms of each methods.