Abstract: The filleted transition surface is a type of surface used to smoothly connect the outer surfaces of objects and eliminate sharp edges. Its construction method is a core technology in both surface modeling and solid modeling. Based on the concept of rolling ball, this study proposes a novel mathematical model for expressing filleted transition surfaces. By explicitly incorporating trimming curves, sphere center trajectories and angle variation into the surface representation, greater flexibility is provided. Within a unified algorithm framework, this model achieves the construction of various transition surfaces, including constant-radius, variable-radius with/without ridge line, three tangent planes, and interpolation-specified curves, through the replacement of local steps. The experimental modeling results show that the quality of the transition surfaces generated by the proposed method reaches the same level as commercial softwares.