Abstract: We present a mathematical analysis for the biologically motivated problem of pressure-driven cellular membrane protrusions, known as blebs. Force balances are used to construct an axisymmetric shell model. This leads to the consideration of non-trivial boundary conditions and a first integral condition. Through weakening the shell over a small region near the axisymmetric tip our aim is to capture characteristic features of the cellular membrane separating from the cortex during the initiation of such protrusions. Further, membrane growth is added, allowing us to maintain a membrane stretch ratio of less than 4%, a fact that has often been neglected in other models. This leads to the conclusion that although blebs are driven by a pressure difference across the cellular membrane it is not the limiting factor in determining bleb size.