In this work, the construction of the cubic spline for the continuous function defined in the segment, as well as the approximation algorithm of the interpolation process and the software for determining the interpolation error were developed. We used cubic splines of the third degree in this work. In the spline definition formula, the value of the coefficient is expressed by the distance between the nodes of the function and the distance between the nodes. The spline-functions method was improved based on the result of analytical analysis to study the methods of approximating functions and functional connections obtained from experience