Deformation is a powerful tool for geometric modeling and design. Such a tool can be used to create a new shape from existing shape without restarting whole design process. A new mathematical model for producing controllable periodic deformations is proposed. By introducing cosine extension functions construct a shape operator matrix and then use the matrix to transform the position vector of some points on the object surface so as to create the deformation effects. Because the cosine extension (Unctions have a number of variable parameters with different properties, the method has corresponding interactive control means. The user can manipulate those parameters to get desirable periodic deformation effects. Experimental results show that the method is feasible and applicable to engineering and research fields such as sheet metal forming by stamping and CAD. A new mathematical model for producing controllable periodic deformations is proposed. By introducing cosine extension functions construct a shape operator matrix and then use the matrix to transform the position vector of some points on the object surface so as to create the deformation effects. Because the cosine extension (Unctions have a number of variable parameters with different properties, the method has corresponding interactive control means. The user can manipulate those parameters to get desirable periodic deformation effects. Experimental results show that the method is feasible and applicable to engineering and research fields such as sheet metal forming by stamping and CAD.