Abstarct: The system of linear and non-linear equations has a wide range of applications in different fields Scientific and engineering such as operational research, physics, economics, civil engineering, electricity and social sciences has it. Solving a system of nonlinear equations when the variables involved are real value systems It has been investigated using different methods. variables or data for easy calculation and Simplicity is considered as clear numbers. However, getting the variables to Clear numbers are not really possible in life problems. Many variables by Some experiments or some experimental uncertainty associated with experimental procedures are found. For example, by measuring the length of a wire with a ruler, we cannot get a clear number Get specifically measured items to the viewing angle of the ruler and the person who measured it It depends. Therefore, the variables should be interval-wise when solving the governing equations be considered Interval calculations are a method to determine error boundaries in mathematical calculations and result It is the development of numerical methods that provide reliable results. Interval calculations for Uncertainty analysis study is used. Also in the field of mathematical modeling and industrial mathematics, numerical analysis, data processing, intelligent systems, control and Optimization is applied. According to the efforts of various researchers to solve the interval of non-system Linear equations, many important information have not been considered in the existing literature. also Some methods are computationally inefficient. The aim of the thesis is to develop some methods For the interval solution of the system of linear and non-linear equations.