Although many years past from presentation of the algorithms for solving integer programming problems, a method, compatible with all of the problems, has not been presented. The aim was on solving the problems with special structures. One of these problems was knapsack problem. This kind of problems was the main focus in last years because of its special theoretical framework and many studies have been done in regard to development of its application and the methods for solving this kind of problems. However some of difficult knapsack problems remain that the offered methods for them are not compatible with these problems. The category of knapsack problems has different kinds and each has its own feature. One of the knapsack problems is the one that the constraint of which is in the form of an equation and is known as equality constraint knapsack problem. In this research firstly the literature related to integer programming and solving related problems was dealt been defined and the methods used for solving these problems has been investigated. In chapter 4, the main idea of this thesis has been described in details. This idea resulted in presentation of two new methods for solving equality constraint knapsack problems. This main idea is actually embedded in the fact that methods like branch and bound and cutting plans are after one goal i.e. finding some nonbasic variables of the primary answer that taking value of them results in getting integreof primary basic variables. In the method presented in this thesis, the focus is on identifying these nonbasic variables in a shortcut way. Since the efficiency of the mentioned methods should be proved, they should be applied to solving sample and standard problems. To this end, these two methods have been applied to 25 equality constraint knapsack problems that are some of the most challenging and difficult problems that have been investigated in several studies as standard problems. The results have been presented in the last chapter. The results are unique in some way and two proposed methods can be very good starting points. Finally a method has been proposed for solving of penalty model, the implication of the main idea and main approach of this study has been proposed as a suggestion in order to presenting new methods for solving integer programming problems, developing and improving two proposed methods in this thesis and popularizing them to knapsack problems.