The tungsten erosion within STEP assuming tungsten main wall and tungsten divertor has been estimated with ERO at the inner and outer divertor, at the inner and outer midplane and at the outboard baffle entrance. Plasma parameters are based on SOLPS simulations applying argon puffing for edge cooling. The modelled peak gross erosion is highest within the divertor with up to 1E19 W /m2/s within the inner and 7E19 W /m2/s in the outer one for the plasma parameter range studied. At the main wall the gross erosion is about 2E18 W /m2/s at the inner midplane and 1.3E17 W /m2/s at the outer one. However, tungsten deposition within the divertor is much larger with amounts between 88% and 98% and only between 10% and 60% at the midplane. At all locations studied, tungsten erosion due to deuterium ions is negligibly small compared to the erosion by argon ions. Erosion due to deuterium atoms has been studied for the outer midplane and is there at least four times smaller than the erosion due to argon ions.