A razor includes a handle, a flexible neck extending from the top of the handle and a blade-carrying razor head pivotally fitted on the distal end portion of the neck. A lower portion of the handle functions as an actuator for dispensing shaving material contained within the handle and is operable between a stop position and a dispensing position. The neck is structured to flex and/or twist in a yielding action in response to external forces as the blade-carrying razor head travels over irregular or varying contours of the skin surface. The flexible neck may be formed to include a scoop for directing a stream of water through the blade-carrying razor head in a fanned array, providing an enhanced flushing action to remove debris and residue which accumulates on the blades.