Quite a few biological systems demonstrate their special functionswith use some hierarchy and discreteness of their structures. Theauthors have revealed the relationship between the toughness andhierarchical ramification structures on interface fracture. In thisstudy, a modified cohesive zone model that deals with a friction lawis applied to quasi-static problems concerning motion of discrete structure ona surface. The problems are analysed by using finite element methodwith frame elements. The sliding properties are investigated fordifferent degrees of freedom (DOFs) of discrete structures. The effectof local structure of branches is examined. By increasing the DOFfor a simple case of microscopic friction law, asynchronous sliding ofthe microscopic structure becomes remarkable. Macroscopic effectivefriction coefficient is studied as well as microscopic deformationmechanism.