A shunt pulsation trap for a positive displacement (PD) internal combustion engine (ICE) reduces pulsation, as well as noise, vibration and harshness (NVH), and the overall size of the exhaust system, and also improves cycle (fuel) efficiency. A shunt pulsation trap for a PD-ICE is configured to trap and attenuate gas pulsations before discharge to engine outlet and includes a chamber (trap volume) adjacent to the PD-ICE cavity. The chamber houses at least one pulsation dampening device, at least one relief port (trap inlet) branching off from the PD-ICE cavity into the pulsation trap chamber and a feedback region (trap outlet) communicating with the PD-ICE outlet. The associated methods of reducing pulsations are included as another aspect of the invention.