In the present work, demonstrate the analytical method to analyze the instability phenomenon by using Laplace transform. For the analysis of instability two phase immiscible flow through the homogenous porous media is adopted. Fingering method is used to develop the Burger’s equation. Which is used to obtain the saturation of water by Laplace transform method. The analytical results show that the saturation of water decreases with an increase in injected fluid and time. The obtained analytical results also satisfied and confirmed from the simulated results that shows the saturation of water.