Two kinds of bivariate basis functions with two shape parameters over the triangular domain were presented. The corresponding triangular surfaces inherited the most properties of classical triangular Bézier surface, and adjusted the shape by changing the value of shape parameters with the fixed control points. When the shape parameters were equal to some specified values, the new triangular surfaces degenerated to the triangular Bézier surface. The obvious geometric significance of shape parameters made it easier for the designer to adjust the shape of new surfaces, even if when the boundaries of triangular surfaces were fixed. The numerical examples indicated that the new surfaces were valid and easy for operation. 