Aim\ The article concerns with the problems of mathematical model formation of free surface and smooth continuity. Methods\ By making use of grid space surface

mon surface

COONS surface

Bezier surface and constructure surface respectively

We can deduce the mathematical equation of free surface

coordinating the condition of Bezier surface\+′s ductibility and the way of arc surface\+′s supplementary point to fulfie the lubricity putting together of free surface. Results\ The way of mathematical formation of free surface and the technology of smooth continuity are put forward. Conclusion\ With some practical value to the problems dealing with the free surface in the process of numerical control program.