This paper is an introduction of terramechanics and its application in off-road vehicle mobility prediction. Firstly the concept of terramechanics is introduced. Terramechanics is an important branch of applied mechanics in which the interaction between the vehicle and its operating terrain is studied. Secondly, many well-known techniques in terramechanics, such as Cone Penetrometer technique, Bevameter technique are introduced. By comparing the RCI of soil with VCI of vehicle, trafficability of Off-road vehicle can be determined which predicts the "go/no go" property of vehicle. Furthermore, to predict the speed behavior of off-road vehicle over trafficable terrain, three types of analyzing methods, empirical, semi-empirical, computer-aided, are presented in detail. It is evident that computeraided method is much more efficient in simulating terrain-vehicle interaction and produces more realistic prediction in vehicle mobility. Therefore, it is meaningful to develop computer-aided method to provide engineers with powerful parametric analysis in vehicle performance and design.