A new contact searching algorithm for general contact systems is proposed in this paper. Due to that the smooth and accurate geometry description is crucial to the contact stress analysis, we have worked out a free-formed-surface (FFS) algorithm specialized to model the contacting surface with the C1 boundary continuity and the exact boundary condition definition. Moreover, the geometrical description using the FFS produces those data required for determining the actual contact direction and calculating the exact contact penetration. Numerical simulation results demonstrate that our contact searching algorithm is robust and capable to simulate three-dimensional contact problems accurately. Copyright.