The numerical solution of singular integral equation (SIE) was summarized

the 2nd type of SIE was solved by piece-wise continuous linear function procedurefor two elastic bodies contact

the SIE was deduced by correlating the slip function and gap function between the two bodies. The contact bodies include the cylinder contact with half space body

parabola shape indentor contact with half space body and tenon contact with mortise cases. These equations were solved by using the piece-wise continuous function method

then contact pressure on the contact surface was acquired. The results of SIE analysis were compared with those obtained from contact theory and finite element method (FEM) analysis. For cylinder contact with half space body

the maximum contact pressure of SIE method is compared with contact theory and FEM

the relative tolerance is 0.3% and 0.5% respectivelyfor tenon contact with mortise

the relative tolerance of maximum contact pressure between SIE method and FEM is 1.8%

proving the effectiveness and applicability of SIE method.