A cover for the upper end of an exhaust stack pipe comprises a curved cover pipe of greater diameter than the stack pipe. The curved cover pipe has a proximal end to fit over the end of the stack pipe and a distal end from which exhaust gases are discharged. The cover pipe is shaped to prevent rain from falling directly onto the end of the stack pipe. A flow diverter of lesser diameter than the cover pipe is mounted within the proximal end of the cover pipe to overlie the end of the stack pipe. The flow diverter comprises an extension tube for mounting onto the end of the stack pipe having lateral openings and a tapering deflector extending into the extension tube to divert exhaust gases to flow into the cover pipe through the lateral openings in the extension tube.