This paper presents a real-time haptic rendering method for multi-contact interaction with virtual environments. Haptic systems often employ physics-based deformation models such as finite-element models and mass-spring models which demand heavy computational overhead. The haptic system can be designed to have two sampling times, T and JT, for the haptic loop and the graphic loop, respectively. A multi-rate output-estimation with an exponential forgetting factor is proposed to implement real-time haptic rendering for the haptic systems with two sampling rates. The computational burden of the output-estimation increases rapidly as the number of contact points increases. To reduce the computation of the estimation, the multi-rate output-estimation with reduced parameters is developed in this paper. Performance of the new output-estimation with reduced parameters is compared with the original output-estimation with full parameters and an exponential forgetting factor. Estimated outputs are computed from the estimated input-output model at a high rate, and trace the analytical outputs computed from the deformation model. The performance is demonstrated by simulation with a linear tensor-mass model.