An experimental study is presented of the flow of elastomers and their compounds in biconical and capillary geometries using rotors and capillaries produced from different materials including aluminum, brass, copper, steel, and stainless steel plus polytetrafluorethylene (PTFE). The rotational rheometer could be operated at various controlled pressure levels. A butadiene–styrene copolymer (SBR) was investigated as well as an SBR compound with 20 vol % carbon black and a second SBR compound with 7% zinc stearate added. It was found in the pressurized rheometer, when the pressure was greater than 0.2 MPa, that the data for SBR and SBR–carbon black was essentially the same for smooth and grooved rotors fabricated from different metals. However when the pressure was reduced the torques were substantially reduced and the data for the grooved rotors were higher than for the smooth rotors. Generally, the copper and brass gave rise to higher shear stresses than the steel or stainless steel. The PTFE yielded the lowest shear stresses. With the compounds containing zinc stearate, the grooved rotors gave higher stresses than the smooth rotors even in pressurized experiments. Experiments are also reported for capillary dies manufactured from different metals. The shear viscosity data obtained in general agree with the pressurized rotational rheometer and a sandwich rheometer, but there is a tendency for higher shear stresses, higher extrudate swell, and more distorted extrudates with the copper and brass dies. The results of the studies indicate that (i) slippage occurs with rubber and rubber compounds at low applied pressure in all systems and at high pressures with certain additives (zinc stearate) and (ii) copper alloys exert higher stresses on unpressurized elastomers or rubber compounds in shear flow than iron alloys. We critique different mechanisms of slippage in the flow of polymer fluids and suspensions.