To overcome the shortages of classic subdivision schemes, a kind of novel semi-stationary push subdivision schemes are proposed. Combined with the advantage of unified subdivision framework, semi-stationary control and push-back operator, the schemes in curve and surface case are given based on subdivision operator. And several limit properties are also discussed. These methods can generate a series of blending shapes between approximation and interpolation of the initial control mesh. In surface case, dire,direction tags are introduced to solve the fairness problem.The extensible schemes based on symbol representation are much useful in computer animation and industrial prototype design application.