An easy-to-assemble modular reamer for medical applications includes a shaft portion, a disposable tapered hollow reamer and a modular pilot. The shaft portion has a proximal end for attachment to a drill, two or more torque transmitting tabs and a distal threaded end. The disposable tapered hollow reamer has an integrally attached cutter sleeve with externally protruding cutters, apertures through the sleeve thickness for discharging bone fragments and cement debris and inwardly protruding anchoring projections. A central molded polymeric portion attaches to the anchoring projection and is fixed to the shaft through central holes and slots in the polymeric portion, which engage torque transmitting shaft tabs. Channels in the polymeric portion collect bone fragments and bone debris. A threaded modular pilot coaxially secures the disposable tapered hollow reamer to the threaded distal end of the shaft, permitting rotation of the tapered hollow reamer without wobbliness.