Palaeostress reconstruction is the key, to quantitative characterization of fractured hydrocarbon reservoirs. In order to calculate the palaeostresses responsible for fault activity, faults in oriented core samples can be analysed and the optimal stresses can then be determined from fault-slip data in a least-squares sense. Many, fractured reservoir rocks, however, include faults generated during a number of different tectonic phases. In these cases, the optimal stresses can be determined for subgroups of faults which are considered to be of approximately the same age. The difticulty with this is that criteria for accurate age-dating are often absent, especially from core samples. Recently, the so-called ''multi-inverse'' method has been proposed to address this problem. This is a numerical technique for separating palaeostresses within a heterogeneousfault assemblage in the absence of a priori information on the faults' relative ages. In this paper, we apply the method to eighteen faults in two short (9m) cores from an exploration well in Hokkaido, northern Japan. The cores came from a fractured hydrocarbon reservoir and were oriented by correlation with borehole images. Core lithologies included massive Cretaceous basalts in which there was no layering which would show fault offsets; for these samples, we determined the sense of shear by, studying would show fault of asymmetric microstructures on the fault surfaces, The results show that the rocks have experienced six different stress regimes. In general, these are compatible with the tectonic history of the study area as inferred,from the regional stratigraphy and from nacroscale geological structures. These results show that the multi-inverse method can be used to extract palaeostress data from cores, thereby, providing information which will assist with the exploration of (and production from) fractured hydrocarbon reservoirs.