Physical phenomena in nature can be modeled with linear or nonlinear differential equations. Different numerical methods are used to solve these equations. In this thesis, the Richards nonlinear differential equation is used to model the flow in unsaturated soils at a section of the road embankment, and the combined local quadrature differential and local triangular differential quadrature (LDQ-LTDQ) methods are used to solve it. The purpose of this thesis is to evaluate the ability of this method to solve the flow in unsaturated soils and to develop a quadrature differential method. Quadrature differential method is a numerical method with high capability and potential. This method is mostly used for problems with regular geometry, and in irregular geometries such as triangular domain, it becomes singular and difficult. To solve these problems, in the triangular area, the triangular quadrature differential method has been used. After discretizing the governing equation by combining the local quadrature differential and the local triangular quadrature differential, the differential equilibrium equations are transformed into algebraic equations. This integrated method has been converted into computer code by MATLAB software and diagrams and counters of pore water pressure in the cross section of the road embankment for different times and for two types of soil with different hydraulic properties have been obtained. These diagrams show the progress of the infiltration front in the depths of the embankment at different times. In order to compare the results obtained from the combined method of local quadrature differential-local triangular differential quadrature, the Richards equation is also solved by finite element method. All the results of the combined method and finite element were compared with the finite difference method of previous researchers. The results show the high compatibility and capability of the DQ-TDQ integrated method in irregular and hybrid geome