Based on the matrix form of triangular Bézier surfaces

the shape modification with geometric constraints is extended from the curve and the tensor product surface to the triangular Bézier surface. The new triangular Bézier surface does not only keep the shape nearly unchanged

but also meets the geometric constraints (multiple position and normal direction constraints). With the help of the Lagrange multiplier method

the conditional extremum problem from the shape modification with geometric constraints is equivalent to solving a system of linear equations. Particularly

the new triangular Bézier surface with the boundary (C

C

C) continuity constraints at three corners also can be obtained. Finally

the numerical examples show the validity and effectiveness in the interactive design in CAD systems.