A tire for a furrow press roller comprises a sole via which the tire is mounted on a field roller support, a tread opposite to the sole, and two sidewalls connecting the tread to the sole. The sole, the tread and the sidewalls together delimit a non-inflatable chamber. The tread comprises at least one crest and two shoulders each connecting the crest to a respective sidewall. The chamber extends partially at least laterally under the shoulders and radially into the crest.