X-ray imaging systems have many applications in medicine, industry and security domains.These systems are divided into several categories based on their performances. In this work the dual energy x-ray imaging system has been considered to determine the effective atomic number of materials interacting with X-ray beam. The process to calculate the effective atomic number is known as materials decomposition algorithm. In this project, according to parameters related to attenuation coefficient, the basic theory used for materials decomposition algorithms was introduced. The physical behavior of photoelectric and Compton elements of the attenuation coefficient in 20-200 keV energy range, typical range of x-ray imaging systems, allows to introduce two-dimensional attenuation coefficient vector space based on fundamental functions and materials. In this work some of these algorithms were studied and simulated by MCNPX and MATLAB codes. These algorithms consist of calibration phase with calibration phantom and the determination phase of Z eff with some mathematical techniques. In this study, the effective atomic numbers of 18 different materials, based on several different algorithms (some calibration phantom and some mathematical technique), were calculated. According to the results, if direct solution is used in sub region area of calibration for the total range, the effective atomic number of materials from light to heavy could be obtained with relative differences of less than 10 percent. For light materials, this method and some other methods including the use of more simple calibration phantom, the direct solution technique estimates the effective atomic number with a relative difference of less than 5 percent. It was also found that use of characteristic angle as an interface quantity, leads to better estimate for the amount of the effective atomic number.