A method of generating cubic spline curves with local shape parameters is presented in this paper．The given method takes the Hermite interpolation curvcs and the cubic non-uniform B-spline curves as the special cases and unifies the representation of the curves interpolating the control polygon and the cubic non-uniform B-spline curves approximating the control polygon．A shape parameter only influences two curve segments，and the expression of the curves retains the simple construction of the expression of the cubic Bezier curves．We can adjust the shape of the curves locally by changing the values of the shape parameters or adjusting the Bezier control points．Based on the given spline curves，the bicubic spline surfaces with local shape parameters are given．