Gram-positive, rod-shaped bacteria, given a pulse of peptidoglycan precursors, first exhibit a lag before the second or turnover phase of peptidoglycan commences. This is because new material is inserted on the inner face of the wall and gradually displaced through the wall. Based on this experimental observation, a mathematical model was constructed and compared with experimental data obtained in several laboratories for the first and second phases of wall turnover of Bacillus subtilis. The model allows the parameters of the process to be estimated for experiments with any labeling time. According to the surface stress theory the wall which is layed down immediately outside the cytoplasmic layer is in an unextended conformation. As subsequent additions of murein occur, the wall moves outward, becomes stretched, and bears the stress due to hydrostatic pressure. Ultimately, peptide and glycosyl bonds become cleaved. At the end of the lag phase the cleavage becomes so extensive that wall fragments are liberated into the medium. This strategy permits rod-shaped growth. In some experimental situations the half-life of wall radioactivity in this second phase roughly equals the doubling time; consequently, the exponential release probably does not represent random turnover but instead is the result of expansion of the underlying wall that continues to create strain which favors autolysis action. The slower turnover of the third phase, where there is a much slower loss, is also included in the analysis.