The bacterial cell wall is a mesh polymer of peptidoglycan – linear glycan strands cross-linked by flexible peptides – that determines cell shape and provides physical protection. While the glycan strands in thin ‘Gram-negative’ peptidoglycan are known to run circumferentially around the cell, the architecture of the thicker ‘Gram-positive’ form remains unclear. Using electron cryotomography, here we show that Bacillus subtilis peptidoglycan is a uniformly dense layer with a textured surface. We further show it rips circumferentially, curls and thickens at free edges, and extends longitudinally when denatured. Molecular dynamics simulations show that only atomic models based on the circumferential topology recapitulate the observed curling and thickening, in support of an ‘inside-to-outside’ assembly process. We conclude that instead of being perpendicular to the cell surface or wrapped in coiled cables (two alternative models), the glycan strands in Gram-positive cell walls run circumferentially around the cell just as they do in Gram-negative cells. Together with providing insights into the architecture of the ultimate determinant of cell shape, this study is important because Gram-positive peptidoglycan is an antibiotic target crucial to the viability of several important rod-shaped pathogens including Bacillus anthracis, Listeria monocytogenes, and Clostridium difficile.