A flushable catheter assembly includes a catheter shaft having proximal and distal end portions. The catheter may include a funnel assembly associated with the distal end portion of the catheter shaft and/or an introducer cap assembly associated with the proximal end portion of the catheter shaft. A groove is defined along at least a portion of an outer perimeter of the funnel assembly or introducer cap assembly, with the groove being configured to receive at least a portion of the catheter shaft for wrapping the catheter shaft around the outer perimeter when disposing of the catheter. Instead of (or in addition to) a groove, one or more channels may pass through the funnel assembly to receive a portion of the catheter shaft for securing the catheter shaft to the funnel assembly for disposal. The catheter assembly and/or its individual components may be formed of a water disintegrable material.