Aqueous solutions of graphene oxide (GO) with a very large average flake aspect ratio, AR = O ( 10 4 ), are probed using capillary breakup experiments and shear rheological measurements for concentrations up to phi = 0.4 vol . %. GO, a chemically oxidized sheet of graphene that we obtained from graphite exfoliation, is suspended in distilled water to produce solutions with volume concentrations spanning 0.02 <= phi <= 0.4 vol . %. For concentrations between 0.1 <= phi <= 0.4 vol . %, the apparent shear yield stress, tau y (determined from creep tests), scales with concentration following a power-law relationship with exponent similar to 2.2. Using capillary breakup extensional rheometry (CaBER), we demonstrate that for concentrations phi greater than or similar to 0.1 vol . %, aqueous GO solutions exhibit power-law fluid behavior in uniaxial elongation. The deformation-rate-dependent transient Trouton ratio over the range where the deformation rates match in shear and capillary breakup experiments is independent of the deformation rate, but inversely proportional to the volume concentration with all values exceeding 3. An attempt is made to estimate the apparent elongational yield stress (for phi >= 0.3 vol . %) by using the Laplace pressure within the fluid filament as its surrogate, and we find that in the strain rate regime that we can observe, the apparent elongational yield stress, tau y , e, is not 3 times the shear yield stress, i.e., for our aqueous GO solutions, we are not able to observe agreement with the von Mises plasticity criterion. GO samples at a given concentration probed in capillary breakup extensional rheology experiments under different protocols, i.e., slow-retraction opposed to step-stretch, exhibited different responses confirming that GO is highly sensitive to the deformation history; however, they still exhibit power-law fluid behavior even given the different initial conditions. Although slightly limited in our ability to quantify the extension-thinning yield-stress-like behavior of aqueous GO in uniaxial elongational flow by the fact that we cannot prescribe the strain rates in CaBER experiments, we demonstrated that even a very small amount of GO flakes can significantly alter the shear rheology and the pinch-off dynamics of a liquid bridge in comparison to Newtonian fluids of equivalent shear viscosity.