The pressure variations observed during an interference test performed in a fractured volcanic tuff are modeled using a stochastic continuum approach. Two sets of spatially heterogeneous conductivity fields are generated. The first one is only conditioned to hard and soft data on conductivities, whereas the second one is also conditioned to transient pressure information. Conditioning to the interference tests introduces an important modification in the conductivity fields, reducing the presumed contrast between the faulted blocks and those that represent the background fracturing. It was possible to reproduce most of the pressure responses simply using a heterogeneous distribution of conductivities without the need to resort to a hydro-mechanical process coupling.