The vibration properties of agricultural tractor’s tyres significantly influence its response in terms of the exposure of the human operator to mechanical vibrations, which is still one of the key problems in the design and exploitation of tractors. The behaviour of the tyre in this sense is significantly influenced by the mechanism ofgeometric filtering of the short-wavelength unevenness of the unprepared ground mostly encountered by tractor during in-field operations. Herein, this aspect of tyre behaviour was studied with tyre rolling quasistatically over singular obstacle. Based on experimental results, neural network based model of tyre enveloping behaviour was developed. Main model properties are high computational efficiency, simplicity regarding number of input quantities and absence of the need for explicit parametrization etc. Main shortcomings of modelling approach used are high developing effort, labour-intensive experimental preparations and lack of flexibility regarding tyre design and operating parameters