The hydrostatic pressure stimulation of an appropriately cell–seeded porous scaffold within a bioreactor is a promising method for engineering bone tissue external to the body. We propose a mathematical model, and employ a suite of candidate constitutive laws, to qualitatively describe the effect of applied hydrostatic pressure on the quantity of minerals deposited in such an experimental setup. By comparing data from numerical simulations with experimental observations under a number of stimulation protocols, we suggest that the response of bone cells to an applied pressure requires consideration of two components; (i) a component describing the cell memory of the applied stimulation, and (ii) a recovery component, capturing the time cells require to recover from high rates of mineralisation.