One-dimensional consolidation of intensely fissured clay masses accounting for fluid exchange between fissures and pores is investigated. As main results, layer thickness does not seem to play the same paramount effect as in classical theories and the use of consolidation coefficients inferred from settlements of small laboratory samples is questioned. For the analysis of pore pressure dissipation, an analog model, made out of elastic springs and pistons inserted in communicating fluid-filled boxes, has been envisioned; the equalizing effect of the saturated porous disc at the base of the sample in a test cell is considered. The behavior of the analog model, discussed on the basis of experimental data, suggests that measurement of interstitial pressures in intensely fissured clays might be affected by important limitations.