Abstract: To constrain the interpolating curves to be bounded in the given region is an important problem in curve design.In this paper,the weighted rational cubic spline interpolation has been constructed using the rational cubic spline with linear denominator and the rational cubic spline based on function values.Because of the new parameters in the interpolating functions,the problems to constrain the weighted rational interpolating curves to lie strictly above or below the given piecewise linear curves (or quadratic curves) and even between them can be solved.