Mating a pair of electric connectors is one of the most important steps in a robotic wiring harness assembly system. A piece-wise linear force model is reported to describe the successful mating process of connectors via elaborate analysis of force during different phases. The corresponding parameter estimation method of this model is also presented by adapting regular least square estimation methods. A typical type of connectors are investigated in this paper. The results can be extended to other types easily. Experiments show that the presented model has good prospects in fault diagnostic tasks.