A continuum model is used for the description of the mechanical response of bilayer lipid membranes (BLMs) subjected to hydrostatic pressure. The model is formulated under the assumption that the BLMs are Smectic A liquid crystals. The mean orientation of the amphiphilic molecules is postulated to be perpendicular to the lipid layers and each layer is idealized as a two dimensional liquid. The permeation process governs the motion of the molecules through the smectic layers. The approach taken in this study is based on the seminal works of Helfrich  and de Gennes  on Smectic A liquid crystals. The failure process of the BLMs, which is observed in the experimental studies, is considered to be due to extrusion of the BLMs through the pores of the polycarbonate filters.