The project treats the cubic spline interpolation and its applications. This method is more appropriate for approximating a given function f(x) by another more convenient function p(x).The Taylor’s polynomial and polynomial interpolation have limitations for approximation of functions. An alternative approach is to divide the approximation intervals into a collection of sub intervals and construct different approximation polynomials on each sub intervals. The cubic spline interpolation is more suitable for approximation of the given function in addition it is applicable in differential equation to solve initial value problems.