An extensive fundamental investigation of the rheological properties and solid wall boundary condition shear stress of elastomers and elastomer–carbon black compounds has been carried out. The elastomers were an emulsion butadiene–styrene copolymer (SBR 1500) and a polybutadiene. Shear flow rheological properties were measured using a newly designed sandwich rheometer, in both constant shear rate and creep modes as well as in a capillary rheometer. A constant elongation rate rheometer for elastomers was developed. Stress relaxation measurements were also carried out in the sandwich rheometer. The shear viscosity of the gum elastomers exhibits a constant very high shear zero viscosity (8 × 108 Pa.s for SBR 1500 at 100°C) and decreases with increasing shear rate. The compounds exhibit yield values of similar magnitude to carbon black compounds of molten plastics. Only the SBR 1500 and its compounds were studied in the elongational flow mode. It was not possible to achieve a steady state in these experiments. An apparatus for measurement of shear stress as a function of velocity (shear rate) at a specified pressure was developed. The instrument, which we call a friction tester, was used not only to determine wall shear stress but to investigate the regime of flow and potentially determine conditions for the onset of slip. Evidence of changing flow regimes were found, and the implications discussed.