When moisture saturated composites are rapidly heated, the steam pressure inside cavities can cause the composite to delaminate. We study the effect of heating rate on the steam pressure inside an isolated long thin “crack-like” cavity of thickness h assuming that the chemical potential of water is continuous across the cavity/polymer interface. For such a cavity in an infinite plate, we show there is sufficient moisture for the steam pressure to reach the saturated steam pressure, irrespective of the heating rate. However, for a plate of thickness L exposed to dry air, the cavity pressure reaches a maximum value, which depends only on the normalized plate thickness, α=L/h and normalized heating rate, β=T˙h2/T0D(T0) where T˙ is the heating rate, D(T0) is the moisture diffusivity at the initial temperature T0, before it decays to zero because of the dry air outside. For this case, the maximum steam pressure can be significantly less than the saturation pressure. The results in this work can also be used to study ‘popcorning’ observed in electronic packages.