New algorithms for the classical problem of fairing cubic spline curves ans bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abonormal portions, the algorithms (automatically or interactively) identify the 'bad' data points and replace them with new pointsproduced by minimizing the strain energy of the new cureve or suface. The proposed algorithms are more general than the existing algorithms in that the new algorithms can adjust more than one'bad' data point in each modification step and they include the existing algorithms in that the new algorithms can adjust more than one 'bad' data point in each modification step and they include the existing algorithms [Computer-Aided Design 15 (5) (1983) 288-293; 28 (1996) 59-66] as special cases. Test results ofthe new algorithms are included.