The invention concerns a tubular-tire for bicycles and its assembly on a mounting-rim of the channel type--that is normally used in combination with the usual tires having a beaded edge.The tubular-tire of the invention has a tunnel-shaped carcass profile, in the plane of the cross-section, provided with a supporting-base which is substantially concave in the center and flat at the sides and with also having two sidewalls that join together in a substantially semicircular vault.The radially inner portion of the sidewalls is joined, at the supporting base, at an angle of less than 90.degree. and it is reinforced with a pair of reinforcing elements--one textile and the other either a textile fabric, or an elastomeric liner.The radially innermost portion of the tubular-tire can be inserted into the channel of a flanged-rim--with thus constituting with said rim, after tire inflation, a stable and inseparable assembly--that proves to be both suitable and efficacious--and with also guaranteeing a qualitatively high road-behavior for the tire.