We use borehole and laboratory measurements with a probe to obtain local permeability estimates. Under ideal conditions sufficiently far from the probe, the flow induced is hemispherical. We describe an experimental apparatus that can flow fluids through a probe under isotropic confining stresses and present an analysis to deduce the optimal dimensions of a finite cylindrical rock to simulate hemispherical flow like that in a semi-infinite medium. We derive equations for permeability interpretation of laboratory measurements. We made pressure measurements on a number of synthetic and natural rocks as functions of confining stress, probe size, flow rate, and flow direction. For synthetic rocks, the calculated permeability shows little dependency on these factors. For natural media, however, flow direction appears to have a major effect at high rates that increases with decreasing probe size. On the basis of these data, we propose a fines-migration mechanism. As expected, permeabilities show a hysteretic dependence on confining stress. Hemispherical flow measurements with homogeneous porous media indicate that fluid injection would yield permeability close to the true value. Furthermore, sequential injection of multiple phases shows that endpoint effective permeabilities may also be obtained.