Tidally induced pore pressure variations below the seafloor depend on the elastic moduli and transport properties of the pore fluid and formation. Hence observations of pore pressure variations, in conjunction with model predictions, can provide important constraints on these formation properties. In this paper, we study the propagation of tidally induced pore pressure variations in a layered poroelastic medium. We derive an analytic solution and use the solution to investigate the effects of various parameters, in particular, the bulk modulus of the formation, the bulk modulus of the pore fluid, and the formation permeability. Specific examples are considered that include the typical continuous depth variation of properties that occurs through normal sediment consolidation and imbedded layers of contrasting properties. Diffusive propagation of tidal pressure variations from the seafloor depends on the hydraulic diffusivity. The depth limit of diffusive propagation scales with the inverse square root of permeability and the period of the signal; for typical fine-grained marine sediments the depth scale at tidal frequencies is only a few meters. Any internal contrast in elastic properties, due to the presence of free gas for example, can give rise to large instantaneous pressure changes across a layer boundary, which in turn can induce diffusive propagation of signals above and below the interface. Long-term pressure records from sealed deep-ocean boreholes that included tidal signals are considered in light of the model results. In Ocean Drilling Project (ODP) Hole 857D on the Juan de Fuca Ridge, the observed attenuation of the seafloor tidal signal to 15% is consistent with the relatively low compressibility of the hydrothermally indurated section intersected by the open part of the borehole and with the high compressibility of the hot formation fluid. In ODP Hole 892B in the Cascadia accretionary prism, the attenuation to 55% and several degree phase lead of the formation tidal signal are probably the result of the open part of the hole being connected to an overlying interval bearing a few percent free gas via a high-permeability fault zone.