In the high resolution satellite images (HRSI), the high accuracy depends on accurate mathematical models for the satellite sensors. Because, there is not satellite orbit information for the most of the new HRSI, this issue is very important in geometric correction of satellite imageries. The pre-processing of satellite images consists of geometric and radiometric characteristics analysis. By performing these operations, it is possible to correct image distortion and improve the image quality and readability. The radiometric analysis refers to mainly the atmosphere effect and its corresponding to feature's reflection, while the geometric correction refers to the image geometry with respect to sensor system with the launch of various commercial high-resolution earth observation systems. However, during the generating of satellite imageries, the projection, the tilt angle, the scanner, the atmosphere condition, the earth curvature and etc., will cause the satellite images to have distortion. So, It is necessary to correction these distortions before one can really use it as a precise measurement in the large scale operations. In this paper, different non-rigorous (generic) mathematical models investigate for geometric corrections over an IRS P6 (Resourcesat-I) Satellite imageries (exactly LISS IV sensor images) in Iran. The LISS IV sensor of the IRS-P6 (Resourcesat-I) satellite has the spatial resolution 5. 8 m with a enhanced spectral resolution. These different geometric models for performing the geometric correction on the satellite imageries includes Rational function models, different orders of polynomials models, projective, affine ( 2D and 3D) and DLT ( Direct Linear Transformation) model with the different numbers of GCP points. Therefore, these mathematical geometric models can be applied to determine the ground point coordinates in object space and so can be used to provide good sufficient insight about the rectified images. In fact non-rigorous mathematical models for geometric corrections of any images can be defined as the models, which can be precisely, present the relationship between the image space and the object space. With implementation of different transformation models on the test data in IRAN, we found the best transformation model in geometric corrections which have the minimum RMSE (Root Mean Square Error) rather than another transformation models.