An excessive demand of vehicles to a motorway bottleneck leads to traffic jams. Motorbikes are narrow and can drive next to each other in a lane, or in-between lanes in low speeds. This paper analyses the resulting traffic characteristics and presents numerical scheme for a macroscopic traffic flow model for these two classes. The behavior included is as follows. If there are two motorbikes behind each other, they can travel next to each other in one lane, occupying the space of one car. Also, at low speeds of car traffic, they can go in between the main lanes, creating a so-called filtering lane. The paper numerically derives functions of class-specific speeds as function of the density of both classes, incorporating flexible lane usage dependent on the speed. The roadway capacity as function of the motorbike fraction is derived, which interesting can be in different types of phases (with motorbikes at higher speeds or not). We also present a numerical scheme to analyse the dynamics of this multi-class system. We apply the model to an example case, revealing the properties of the traffic stream , queue dynamics and class specific travel times. The model can help in showing the relative advantage in travel time of switching to a motorbike.