Following Atkinson and Crasler (Proc. R. Soc. Lond. A434, 605–633, 1991). Craster and Atkinson (J. Mech. Phys. Solids, accepted. 1992). we consider the problem of quasi-static plane strain fracture at the interface between different linear isotropic elastic diffusive solids i.e. fully coupled poroelastic and thermoelastic materials. The problem of quasi-static growing cracks or the initiation of fracture between the materials is of particular interest. In fabricated materials there is a possibility of imperfect bonding or welding, hence fracture is often initiated near or at the interface. We consider here the slightly simpler case when one of the materials is rigid and the interface is either completely permeable (conducting) or impermeable (insulated). Such an assumption about the interface is common in geophysics and is relevant to the ease of two completely different materials welded together in industry.The solution for impulsively opening cracks is considered here using general potential solutions of the poroelastic (thermoelastic) equations used together with Laplace and Fourier transforms. Solution then proceeds by use of the Wiener Hopf technique; the resulting transformed results are then examined in the neighbourhood of the crack tip. The oscillatory singularity, as calculated by Williams (Bull. Scismol. Soc. America49, 199–204. 1959) for interfacial fracture in linear isotropic elasticity, is recovered as a particular case. This oscillatory singularity which predicts interpenetration of the crack walls (England, ASME J. Appl. Mech.32, 400–402, 1965) need not lead us to disregard the solution, although it invalidates the results on the scale of the contact zone. Provided this zone is much smaller than the crack length, the results are still valid for the zone near the crack tip.A contact zone model of the Comninou (ASME J. Appl. Mech., 1977) type is then developed. The oscillatory solution is then used as an outer solution in the method of matched asymptotic expansions as in Atkinson (Int. J. Fracture18, 161– 177, 1982a; Int. J. Fracture19, 131–138, 1982b); this is then matched with an appropriate inner solution to correct for the unphysieal interpenetration of the erack walls. This approach is valid for small contact zone lengths due to the interpenetration effect.The problem of steadily propagating fracture is also briefly considered and the stress intensity factors and distinctive near erack tip pore pressure fields are evaluated.