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SOXS is a new spectrograph for the New Technology Telescope (NTT), optimized for transient and variable objects, covering a wide wavelength range from 350 to 2000 nm. SOXS is equipped with a calibration unit that will be used to remove the instrument signatures and to provide wavelength calibration to the data. The calibration unit will employ seven calibration lamps: a quartz-tungsten-halogen and a deuterium lamp for the flat-field correction, a ThAr lamp and four pencil-style rare-gas lamps for the wavelength calibration. The light from the calibration lamps is injected into the spectrograph mimicking the f/11 input beam of the NTT, by using an integrating sphere and a custom doublet. The oversized illumination patch covers the length of the spectrograph slit homogeneously, with $< 1\%$ variation. The optics also supports the second mode of the unit, the star-simulator mode that emulates a point source by utilizing a pinhole mask. Switching between the direct illumination and pinhole modes is performed by a linear stage. A safety interlock switches off the main power when the lamp box cover is removed, preventing accidental UV exposure to the service personnel. All power supplies and control modules are located in an electronic rack at a distance from the telescope platform. In this presentation we describe the optical, mechanical, and electrical designs of the SOXS calibration unit, and report the status of development in which the unit is currently in the test and verification stage.