Focusing our attention on the cell wall and the plasmalemma (i.e. the cell membrane), we seek to show that the initiation of the regenerative, growing tip in the unicellular marine alga Acetabularia mediterranea, can be predicted using the techniques of thin-shell and elasticity theory. We build upon and extend the work of Goodwin & Trainor (1985, J. theor. Biol. 117, 79–106), Trainor & Goodwin (1986, Physica D. 21D, 137–145) and Brière & Goodwin (1988, J. theor. Biol. 131, 461–475) where the attention was focused on the calcium-regulated strain and stress fields of the cortical cytoplasm. Finally, we attempt to model the subsequent tip growth using a moving-boundary formulation, with cytosolic free calcium concentration and turgor pressure being the two variables responsible for the growth.