Single-use syringe in which the barrel has walls of variable thickness in the cross section thereof but walls of constant thickness longitudinally. The barrel is cylindrical, with a circular end wall externally, and, within, the chamber for the injectable liquid has different forms. The barrel furthermore has, on the inner walls thereof, an upper groove and a lower groove close to the end of the barrel where the needle is located. A close-fitting plunger with longitudinal fins, each with a constant height along the entire length thereof, slides inside the barrel.