A Weissenberg rheogoniometer was modified1-3 to improve sample temperature uniformity and constancy (to within ±0.5°C) and to give a quicker response to normal thrust changes (estimated gap change ≤0.1 μm/kg thrust; gap angle = 8.046°; gap radius = 1.2 cm; servomechanism replaced by an open-loop cantilever spring of 10 kg/μm stiffness). Low-density polyethylenes (IUPAC samples A and C, melt index at 190°C = 1.6) at 150°C were used in step-function shear rate experiments. Inspection of marked sectors in the samples showed substantial uniformity of shear at values of Ṡ = 0.1, 2, and 5 sec−1; for Ṡ = 10 sec−1 and S ≤ 2 shear units (S = Ṡt), the shear was highly nonuniform at and near the free boundary. Using selected premolded samples A, scatter in seven replicate tests at Ṡ = 1.0 sec−1 did not exceed ±6% for N1(t) and ±5% for σ(t) (N1 = primary normal stress difference; σ = shear stress; t = time of deformation from the initiation of experiment at zero time). N1(t) and σ(t) data agreed with Meissner's1; for Ṡ = 0.1, 2.0, 5.0, and 10.0 sec−1, torque maxima occurred at S = 6 shear units, and thrust maxima occurred in the range of 10 to 20 shear units. σ(t) and N1(t) data do not satisfy the van Es and Christensen4 test for rubber-like liquids with strain rate invariants included in the memory function. On cessation of shear (after a shear strain S at constant shear rate Ṡ), initial values of −dσ(t)/dt and −dN1(t)/dt were found to depend strongly on S, in some cases passing through maxima as S was increased. After shearing at Ṡ = 0.1 sec−1 for 500 sec, such that stresses became constant, stress relaxation data satisfied Yamamoto's5 equation of dN1(t)/dt = −2Ṡσ(t).