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.