An easy-to-assemble modular tapered or spherical reamer for medical applications includes a shaft portion, a disposable tapered or spherical hollow reamer and a guide pin. The shaft proximal end attaches to a drill and the distal end has a tapered body element with a tapered external surface and a central aperture. The disposable tapered or spherical hollow reamer has a central aperture that accepts the guide pin and an interior taper that matches the taper of the tapered body element. The guide pin has attachment means to attach its distal end to the central aperture in the reamer, and the proximal end to the central aperture of the tapered body element of the shaft, assuring reamer/shaft concentricity. Contact between the reamer taper and the taper of the tapered body element aids this concentricity. Torque transmission between the shaft and the reamer is accomplished by torque transmitting tabs or a threaded connection.