The top wall of a snowmobile tunnel, which accommodates the endless drive track of the snowmobile, is provided with recesses at locations corresponding to the path followed by studs carried by the endless track. In another aspect of the invention, the rear of the tunnel is connected to a molded rear member. The rear member provides a downwardly curving back portion for the tunnel. The rear member may have a shape corresponding to that of the tunnel, e.g. having a pattern of recesses matching that of the top wall of the tunnel. In yet another aspect of the invention, a heat exchanger for cooling engine coolant may be provided at the rear of the tunnel. The heat exchanger may be mounted to and partially spaced from the molded rear member, thereby permitting snow thrown by the endless track to pass on both sides of the heat exchanger. In another aspect of the invention, a tunnel for a snowmobile may be narrower in the front than in the rear.