Biaxial straining has been done by first producing a uniformly thinned, elongated patch at the center of a much larger metal sheet. The patch was gridded with 100 lines per in, separated from the loading tool with an annular spacer of polyethylene, and then deformed incrementally by stretching the sheet over a large-radius hemispherical punch. By regulating patch eccentricity, the imposed strain ratio,ρ =e 2/e 1, could be made nearly constant over a range from slightly less than zero to ∼0.6. Strain at first developed uniformly throughout the patch. But gradually a perturbation in ∈ became apparent and rather quickly after thatδe 2/δe 1 → 0 as a local neck and finally a tear appeared. A clear indication of the straine 1 * at whichδe 2 δe 1 → 0 for any given ρ could be found in the results. The test materials were an aluminum-killed steel (both annealed and cold rolled), copper (in three grades and with different grain sizes), α-brass, type 301 stain-less steel, and Zircaloy-4. A range of behavior was observed. In most cases,e 1 * at ρ=0 was less than predicted by the usual instability theory, andρ = 0 was either <0 or ≃0. The ferritic steel was unique in supporting conventional theory at ρ=0 and having a large, positivede 1 * /dρ. A theory of quasistable flow, which recently entered the literature, was applied to the results, but with indifferent success. The central problem seems to be one of identifying the structural origins of the small-scale weakness that underlies the gradual local change from a uniformly imposed ρ to ρ=0.