Presently there is quite few analytical studies in traffic flows due to the non-linearity of the governing equations. In the present paper we introduce travelling wave solutions for the homogeneous one-dimensional FREFLO model, which are expressed in the form of series and describe the procedure that vehicles/pedestrians move with a negative velocity and decelerate until rest, then accelerate inversely to positive velocities. This method is expect to be extended to more complex situations in the future.
