Spontaneous imbibition (SI) is a very important oil recovery mechanism from low-permeability fractured reservoirs. The impact of different sample shapes and boundary conditions on oil recovery by counter-current and co-current SI into low-permeability (approximate to2 mD) strongly water wet outcrop chalk have been investigated. The experimental program was divided into two parts. In part 1, counter-current SI was studied by submerging cubic, cylindrical, and irregular rock samples totally in the aqueous phase, whereas co-current SI was investigated in part 2 by exposing different portions of a cubic rock sample to an oil-phase. The scaling law of Ma et al.(1) was used to correlate counter-current SI data with all parameters than the characteristic length, L-C, held essentially constant. The results confirm the ability for L-C to account for cylindrical (diameters in the range from approximate to2 to 10 cm) and cubic sample shapes and different no-flow surface boundary conditions (2, 4 and 5 faces were coated with polyester on the cubic rock samples; top and bottom faces on the cylindrical cores). Rock samples having irregular shapes (increasing and decreasing cross-sectional areas were investigated) could not be scaled according to L-C because the overall shape of the imbibition curves deviated from curves generated by rock samples having regular shape. No scaling law correlating imbibition data for different boundary conditions exists for tests performed under co-current flow conditions; hence the results in part 2 of the experimental program are interpreted qualitatively. When using the SI rate for a cube with all faces open to imbibition as the reference (counter-current flow conditions), the results show that depending on the area fraction of the cube covered by oil, co-current SI can either be faster (water-oil area ratio (WOAR > 1), equal (WOAR = 1) or slower (WOAR < 1)) than the reference system. In all cases, ultimate recovery is significantly higher for tests performed under co-current flow conditions than under counter-current (70% of initially oil in place IOIP) vs 58% IOIP for counter-current). The results indicate that when evaluating oil recovery potential on reservoir rock samples due to SI experimentally, tests should be performed both under co-current and counter-current flow conditions because the latter one might under certain circumstances predict too low rates and ultimate recoveries.