A pneumatic tire has a non-stretchable tread (30) flanked by two shoulder regions (34), and two non-stretchable bead regions (36) for mounting the tire to a wheel, each bead region being connected via a sidewall to the corresponding bead region. Each sidewall has a first portion (38) extending inwardly relative to a width of the tire from one of the bead regions (36) to a deflection region (40), and a second portion (42) extending outwardly relative to the width of the tire from the deflection region (40) to a corresponding one of the shoulder regions (34). A non-stretchable girth-limiting configuration (44, 46, 56) and a radial reinforcing structure (48, 50, 52) are associated with the first portion (38) of each of the sidewalls, thereby limiting radial flexing of first portion (38) and maintaining an annular concavity between the bead region (36) and the shoulder region (34).