This paper describes a new method for generating surfaces of branching tubular structures with given center-lines and radii. As the centerlines are not straight lines, the cross-sections are not parallel and well-known algorithms for surface tiling from parallel cross-sections cannot be used. Nonparallel cross-sections can be tiled by means of the maximal-disc interpolation method; special methods for branching-structures modeling by means of convolution surfaces produce excellent results, but these methods are more complex than our approach. The proposed method tiles nonparallel circular cross-sections and constructs a topologically-correct surface mesh. The method is not artifact-free, but it is fast and simple. The surface mesh serves as a data representation of a vessel tree suitable for real-time virtual reality operation planning and operation support within a medical application. Proposed method extracts a "classical" polygonal representation, which can be used in common surface-oriented graphic accelerators