There are large number of phenomena in the universe show non-extensive behavior and therefore Boltzmann-Gi statistics can’t describe them, therefore non-extensive statistics, such as Tsallis statistics is the only way to study them. This thesis has been fouced on the extraction of equation of state for nonextensive systems. In fact, the basis of this research isto extract the partition function, equation of state and evaluation of thermodynamic properties for ideal gas, hard sphere and Lenard-Jones fluid in the fourth version of Tsallis statistical mechanics (OLM formalism) for q more than one. Wehave obtained that the partition function for all models in Tsallis statistics for q more than one is more than their corresponding values in Boltzmann-Gi statistics. We have also shown that the compressibility factor for ideal gas in Tsallis statistics is lower than its value in Boltzmann-Gi statistics. Thisstudy has also shown that the internal energy in OLM formalism for ideal gas is equal to . This result obtains without invoking the limit q 1. Evaluating compressibility factor for hard sphere fluids is show that this factor in Tsallis statistical mechanics is more than its values in Boltzmann-Gi statistics.Theinternal energy for Lenard-Jones fluids in spite of two previous models is dependent on the entropy index , q . Evaluating the compressibility factor for Lenard-Jones fluid show that this factor in Tsallis statistical mechanics is more than its values in Boltzmann-Gi statistics.