For ground robots, the mechanical properties of certain terrain, such as muddy ground, negatively affect the locomotion performance and trafficability. In order to obtain a compact and efficient underlying representation of the terrain mechanical properties, in this paper, we propose a new method based on learning that has two remarkable advantages: 1) It establishes the relationship between specific positions and their corresponding mechanical properties, which is represented by a parametric model learnt from mechanical properties data. The model can query terrain mechanical properties of an arbitrary point. 2) It's a highly memory-saving underlying representation of terrain mechanics for the parameters of the learnt model are finite, that is, the needed memory is very little. The proposed approach, called Hilbert terramechanics map, is based on the computation of kernel approximation that projects the data into a Hilbert space in which a multiclass logistic regression classifier is learnt by fast stochastic average gradient descend. We demonstrate the advancements of our method on two simulated environments which are very close to the real world.