Abstarct: Delay differential and integral equations (DDIEs) have a wide range of applications in science and engineering. When these equations are nonlinear, we cannot usually obtain an exact solution. Hence, we must utilize an efficient numerical method with high convergence rate and low error to approximate the solution. In this thesis, we propose a new shifted pseudo spectral method to solve different classes of DDIEs. First, we transform the problem into a nonlinear programming (NLP) problem and then utilize a pseudo spectral method to discrete the problem. After solving this discrete problem, we can achieve the pointwise and continuous approximate solutions for the main DDIES. We analyze the convergence of the suggested methods for DDIEs. Moreover, by solving some practical DDIEs and comparing the method with some other methods, we show the efficiency of the method.