Summary: In designing running mechanism of a tracked vehicle running on off-road, the sinkage of the vehicle should be predicted by some methods to optimize the running mechanism. The empirical models for the sinkage prediction have been proposed by Bekker, Reece, etc, to express the relationship between pressure on a plat and sinkage of the plat. In order to verify the accuracy of these empirical models, seven plates with similar load and contact area but different dimensions of length and width were employed as well as a new pressure sinkage measurement system equipped by a manipulator. The results of the tests show that these empirical models are not always coincident with the real situation. This paper proposed a new method to predict the sinkage of a plat more accurately, by using fuzzy neural network. Because the soil parameters and the load exerted on the plat are ambiguous, we propose a fuzzy prediction method using possibility function to express the distribution of the sinkage. The methods proposed in this paper are verified by real pressure-sinkage tests.