With the emergence of Covid 19, researchers have begun to address the spread of the disease from various perspectives. Some researchers have focused on statistical analysis to model these problems by fitting the data set or performing stability analysis to construct a theoretical frame-work for the solutions of these mathematical models. After all, they finalized their studies using a numerical technique to confirm that the model accurately depicts how the disease progress-es. For this purpose, Runge Kutta methods are widely used in the literature as numerical tech-niques, because of their easy implementation. However, these methods do not explicitly pro-vide approximate solutions for problems with no exact solution; thus, their accuracy cannot be discussed through error analysis. Therefore, this study deals with a numerical investigation to find approximate solutions of the Susceptible-Infected-Removed model for Covid 19 spread in Türkiye, using Chebyshev, Legendre and Laguerre polynomials. These polynomials can be easily implemented without the need for discretization and are effective in solving systems of nonlinear ordinary differential equations. The main idea of the method used in this study is to approximate the solution and its derivatives using a truncated series of orthogonal polynomials and convert the differential equation system into an algebraic equation system. Then, the obtained system is solved using MATLAB for unknown coefficients, which results in an approximate solution. To demonstrate the implementation of the method, the model is considered with official data regarding the course of Covid 19 in Türkiye. The obtained approximate solutions are compared with the other numerical results in figures and tables, and highly accurate results are obtained such as absolute errors and residual errors being around 10-10. Therefore, this method, based on orthogonal polynomials, can be adopted to address more challenging real-life problems.