The flow regime is identified as a steady-state flow if the pressure at every location in the reservoir remains constant. In this work, we have determined the well production rate and cumulative production in a circular reservoir using the Finite Element Method for the condition of constant pressure outer boundary. The reservoir was divided into 4 smaller part known as finite element. These parts were analyzed and later assembled to form the domain of the reservoir. The analysis was done with the assumption that before the well begins production, there was uniform distribution of pressure all through the reservoir. The results obtained from the production rate analysis shows that the dimensionless production rate decreases significantly and later becomes uniform because the withdrawn fluid has been completely replaced. This condition remains throughout the entire life of the reservoir presumably. Also, the result shows that there is a uniform increase in the dimensionless cumulative production as time increases. The result obtained in this work was compared with the results obtained by previous researcher. The comparison shows a strong positive correlation between the two methods with a maximum percentage error of 0.1711 and 0.1864 and a minimum percentage error of 0.0001 and 0.0122 for dimensionless production rate and dimensionless cumulative production respectively. Also, result from previous researcher only state the production rate and cumulative production of the reservoir at a particular time but this work predicts the production rate and cumulative production in the entire reservoir at the same time.