Unplug the Eureka's power cord from the wall outlet.
Press the foot switch on the base of the Eureka to unlock the upper half of the vacuum, which can now tilt up and down at an angle. Turn the appliance upside down and place it on a flat surface.
Take out the screws in the housing cover to open the vacuum. The cylindrical motor is located near the bottom of the upright. Two wires connect to the top of the motor and a drive shaft extends from the bottom.
Pull the two wires off the terminals on the motor using pliers. Depending on the age of the appliance, the wires may be welded to the motor terminals on some models. Use wire cutters to cut the wire as close as possible to the motor terminals.
Loosen the clamp on the hose where it attaches to the side of the motor, using a screwdriver. Pull off the hose.
Remove the screws in the motor housing that hold it against the braces inside the Eureka.
Pull the motor upward at an angle to disengage it from the housing. Slide the belt off the end of the wheel on the motor drive shaft. You can now remove the motor from the Eureka to install a replacement.