This paper deals with the modeling of G 1 bifurcation. A branch-blending strategy is applied to model the bifurcation such that the coherence among the individual branching segments is characterized. To achieve this, bicubic BΓ©zier patches are first used to generate three half-tubular surfaces by sweeping operations. The bifurcation modeling is then converted to a problem of filling two triangular holes surrounded by the swept half-tubular surfaces. In order for the bifurcation model to be G 1 , the candidate surfaces for hole filling are required to have (i) an inter-patch tangential continuity along the so-called star-lines; and (ii) a cross-boundary tangential continuity with the surrounding half-tubular surfaces. For inter-patch tangential continuity, we use the method proposed by Gregory and Zhou (1994) to determine the center-point, the star-lines, and the associated vector-valued crossboundary derivatives. The problem of ensuring the cross-boundary tangential continuity with the surrounding surfaces is more difficult. We first derive the conditions for the twist-compatibility from the requirements of crossboundary tangential continuity. The solutions for the conditions derived are then developed. The hole boundaries, originally in cubic BΓ©zier form, are constructively modified to the quintic form to ensure the twist-compatibility and uniqueness of the tangent planes at the hole corners. Subsequently, the half-tubular surfaces in bi-cubic BΓ©zier form are degree-elevated to quintic form along the sweeping directions. This is followed by the modification of the second row control points with the half-tubular surfaces in order to retain a cubic form of the surfaces' crossboundary derivatives. Vector-valued cross-boundary derivatives in quintic BΓ©zier form are constructed for the hole patches. Using a Coons-Boolean sum approach, the derivatives are utilized to modify the three BΓ©zier patches into the final bi-quintic form in the triangle fill area for each hole.