A finite element solution for multibody contact problems is presented. Contact conditions being exactly introduced

this solution takes nodal contact forces as primary variable and limits contact highly nonlinear problem in potential contact surfaces to iterate

so it is an accurate and high efficient approach. The paper begins with 3D mechanical model for two bodies contact and compatibility equation in incremental form is educed from global finite element equation. On this basis how to obtain compatibility equation on multibody contact problems is discussed in detail. Subsequently

solvable and judged conditions in incremental form of contact problems are presented in which generalized Mohr-Coulomb criterion is used as friction condition. For the characteristics of any slipping direction of contact nodes on the contact interface in 3D case

contact states and friction force components are judged simultaneously in the program by which iteration and convergence are fast and accurate. For the common non-smooth contact namely corner problems in the more contacting bodies

more reasonable techniques are proposed by classification and real contact state of corners. Finally

after being verified by several numerical examples the program is employed to model rock discontinuities; and the results are satisfactory.