Aims:We analyze the distribution of the interstellar matter in the environs of the H ii region Gum 31, excited by the open cluster NGC 3324, located in the complex Carina region, with the aim of investigating the action of the massive stars on the surrounding neutral material. Methods: We use neutral hydrogen 21-cm line data, radio continuum images at 0.843, 2.4 and 4.9 GHz, 12CO(1-0) observations, and IRAS and MSX infrared data. Results: Adopting a distance of 3 kpc for the H ii region and the ionizing cluster, we derived an electron density of 33±3 cm-3 and an ionized mass of (3.3±1.1)×103 M&sun; based on the radio continuum data at 4.9 GHz. The H i 21-cm line images revealed an H i shell surrounding the H ii region. The H i structure is 10.0 ± 1.7 pc in radius, has a neutral mass of 1500 ± 500 M&sun;, and is expanding at 11 km s-1. The associated molecular gas amounts to (1.1 ± 0.5)×105 M&sun;, being its volume density of about 350 cm-3. This molecular shell could represent the remains of the cloud where the young open cluster NGC 3324 was born or could have originated by the shock front associated with the H ii region. The difference between the ambient density and the electron density of the H ii region suggests that the H ii region is expanding. The distributions of the ionized and molecular material, along with that of the emission in the MSX band A, suggest that a photodissociation region has developed at the interface between the ionized and molecular gas. The copious UV photon flux from the early type stars in NGC 3324 keeps the H ii region ionized. The characteristics of a relatively large number of the IRAS, MSX, and 2MASS point sources projected onto the molecular envelope are compatible with protostellar candidates, showing the presence of active star forming regions. Very probably, the expansion of the H ii region has triggered stellar formation in the molecular shell.