Summary: The SIR model is a mathematical model of epidemics involving the unknowns Susceptible, Infected, and Recovered. We consider a numerical solution of the Fuzzy SIR model (FSIR) with fuzzy initial conditions. Actual values of the parameters are used for the Kingdom of Saudi Arabia region for the peak period of July-August 2020 for COVID-19. Due to the nonlinearities in the SIR model and the included fuzzy concepts, the solution methods are focused on numerical techniques. The Euler method is the simplest numerical technique with minimum function evaluation per step which is an effective factor in a fuzzy environment. The results show the effective impact of lockdown policies. Moreover, the fuzzy concepts give global attitudes about the components of the SIR model. Furthermore, we establish a graphical representation of the actual documented data with the solution of the FSIR model for the data of our sample for different values of the fuzzy parameter.