A general and efficient algorithm is proposed for the analyses of multibody elastic contact problems. It is presumed that there exists negligible friction between the bodies. It utilizes a simplex type algorithm with a modified entry rule and incoporates finite element method to obtain flexibility matrices for arbitrarily shaped bodies. The multibody contact problem of a vehicle support on an elastic foundation is considered first to show the effictiveness of the suggested algorithm. Its solution is compared favorably with the existing solution. A contact problem among inner race, rollers and outer race is analyzed and the distribution of load, rigid body movements and contact pressure distributions are obtained. The trend of contact characteristics is compared with that of the idealized Hertzian solutions for two separate two-body contact problems. The numerical results obtained by directly treating a multibody contact are believed to be more exact than the Hertzian solution for the idealized two separate two-body contact problems.