In the oil and gas industry, it has been estimated that in excess of US$ 500 millions [7] is losteach year because of wellbore instability. To prevent problems due to wellbore instability,accurate prediction of stress and deformation around the wellbore are essential. Laboratorytests on thick-walled hollow cylinders of rock are a relatively easy, economical and realisticmeans to better understand the mechanisms associated to wellbore failure.The first part of this research consisted in the development of an experimental device to carryout tests on thick-walled hollow cylinders under two distinct conditions:1) Tests without pore fluid (to simulate the underground opening during and after thedrilling).2) Tests with convergent radial flow of pore fluid (to simulate the wellbore during itsphase of production). The latter is one of the key advantages of this experimental devicesince this possibility of radial flow does not exist in the majority of studies reported in theliterature.The second part of this research discusses the experiments carried out on the rock-likeceramic material called CPIR09. The behaviour of this material is similar to very poroussandstones which form certain oil reservoirs. The mode of rupture observed in the tests was apair of radial rupture planes that are diametrically opposed (parallel with the axis of the holeand perpendicular to the internal wall) which corresponds to a compacting failure mechanism.The results obtained show that the global permeability decreases with increasing externalpressure. The convergent radial flow of pore fluid does not affect the form of the rupture butacts to remove fractured materials to erode localization bands. The convergent radial flow ofpore fluid (due to the imposed pore pressure) may slightly decrease the strength of the samples.