A machine for wrapping a strap in one or two loops around a package has a support frame and first and second upright generally annular strap-guiding channels. The channels each have confronting ends defining a respective gap that are immediately adjacent each other, and the package is engageable within the annular channels. A single-loop guide fittable in the gap of the first channel has a guide groove extending in a single-loop mode between the ends of the first channel. A double-loop guide fittable in a dual-loop mode in the gaps of the first and second channels has first and second crossing guide grooves that extend between one of the ends of the first channel and one of the ends of the second channel and the second guide groove extending between the other of the ends of the first channel and the other of the ends of the second channel.