The instrument (1) has a core (7) made of a flexible elastic material and exhibiting a memory model. A coating (8) is provided with abrasive particles such as ceramic particles and diamond particles, on the core. The flexibility of the coating is matched to the flexibility of the core. The core is made of a nickel-titanium alloy or a fiber-reinforced plastic. A proximal end (10) of the core has a grinding or polishing body with the abrasive particles. The core is made of carbon fibers embedded in an adhesive mass of polypropylene, polyethylene or epoxy resin. The abrasive particles are ceramic particles and diamond particles, corundum particles, boron nitride particles, boron carbide particles, silicon particles, silicon nitride particles and/or silicon carbide particles. An independent claim is also included for a method for manufacturing a root canal instrument.