The shape of walled cells such as fungi, bacteria, and plants are determined by the cell wall. Models for cell morphogenesis postulate that the effects of turgor pressure and mechanical properties of the cell wall can explain the shapes of these diverse cell types. However, in general, these models await validation through quantitative experiments. Fission yeast Schizosaccharomyces pombe are rod-shaped cells that grow by tip extension and then divide medially through formation of a cell wall septum. Upon cell separation after cytokinesis, the new cell ends adopt a rounded morphology. Here, we show that this shape is generated by a very simple mechanical-based mechanism in which turgor pressure inflates the elastic cell wall in the absence of cell growth. This process is independent of actin and new cell wall synthesis. To model this morphological change, we first estimate the mechanical properties of the cell wall using several approaches. The lateral cell wall behaves as an isotropic elastic material with a Young's modulus of 50 ± 10 MPa inflated by a turgor pressure estimated to be 1.5 ± 0.2 MPa. Based upon these parameters, we develop a quantitative mechanical-based model for new end formation that reveals that the cell wall at the new end expands into its characteristic rounded shape in part because it is softer than the mature lateral wall. These studies provide a simple example of how turgor pressure expands the elastic cell wall to generate a particular cell shape.