The algebraic properties of curves and surfaces are directly determined by its form of parameter, such as regularity. However, in computer aided geometric design, the phenomenon of self-intersection belongs to a kind of irregularity problem which cannot be applied directly. The tubular surface, as a kind of important geometric model, mainly studiing pipe surfaces and orthogonal torus. On the basis of researching the regular tubular surface, we must attach important to researching self intersection of two kinds of special irregular tubular surfaces. The paper mainly applies algebraic methods to analyze their geometric features respectively, so as to specify some areas of self-intersection in theory. Furthermore, it can provide support to remove self-intersection exactly in the future.