Recent technology advances in the field of ride-by-wire technology for motorcycle (namely active braking and full electronic throttle) open the way to the design of innovative control strategies to improve two-wheeled vehicles stability. As such, it is of growing importance to devise control oriented models of the bike dynamics to be employed for control design purposes. This paper proposes an analytical model of a two-wheeled vehicle tuned to capture the coupling between longitudinal variables (i.e. traction and braking torque) and out-of-plane modes. The model is derived from first principles. The model parameters are identified from a complete multi-body simulator. The proposed model offers a good tradeoff between complexity and accuracy