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This paper investigates the Numerical solution nonlinear partial differential equation for one dimensional instability
phenomenon known as Boussinesq's equation arising in a porous media in oil-water displacement treatment (instability). Its
Numerical Solution has been acquired by utilizing B-Spline method with proper boundary and initial conditions. The Numerical
solution of Boussinesq's equation using Spline method is very nearer to Exact Solution obtained by analytical method .It is
surmise that when distance and time increases, its saturation of injected water is increases . Numerical solution and graphical
illustration has been obtained by Matlab.