The paper describes the model implementing the lateral dynamics of the TTW vehicle and the stability analysis performed in straight running. The complexity of the layout and the goal of taking into account the main dynamic effects outlined in the recent literature on motorcycle dynamics suggested adopting a multi-body approach. To this end, the implementation was done in Matlab/Simulink/SimMechanics environment while an Adams-Motorcycle model was adopted for cross-validation. An equivalent motorcycle four degrees-of-freedom model was used to evidence the effects that can be predicted with such a simplified analytical model and to highlight the similarities in terms of stability between a motorcycle and a tricycle like the TTW. Tests performed on a test track were carried out to get sensitivity on the stability of the vehicle, tune some model parameters, identify the damping on the steering axis and prove the validity of the model. The stability analysis leads to the following conclusions: (1) The vibration modes and the issues on the stability of the TTW are similar to that of a motorcycle. (2) As in motorcycles, the vertical and lateral dynamics are uncoupled in straight running. (3) The effect of the lateral and torsional chassis compliance on the modes involving the motion of the front body is not dominant, as in motorcycles being the frame stiff enough and the elastic axis of rotation close to the ground. (4) The decay rate of the wobble mode is very sensitive to the CT so that a fine analysis of its value must be followed when designing the vehicle to guarantee stability. (5) The out-of-phase motion of the front wheels seems to be weakly coupled with the weave and wobble modes in straight running. This consideration will be verified with further analysis. If it will be confirmed, it will be possible to conclude that the track of the wheels does not influence the lateral stability of the vehicle in straight running. Excluding the remark 3 that is mainly related to the particular configuration of the TTW, the results obtained in the present paper and those summarised above can be extended to all the free tilting tricycles and quadricycles in which the suspension kinematics enables the vehicle body to roll in parallel with the wheels.