The NuSTAR (Nuclear Spectroscopy Telescope Array) observatory (Harrison et al. 2009), expected to be launched into an equatorial low earth orbit in 2011, will have two mirror assemblies capable of imaging X-rays in the hard X-ray band between 5 keV and 80 keV. It will be the first X-ray observatory using multilayer coatings to significantly expand the bandwidth of the typical X-ray telescope of 0.1 keV to 10 keV. The mirror assemblies use a segmented design to simplify the construction process, as such they require 4,680 mirror substrates coated with appropriately designed multilayers to enhance reflectivity for hard X-rays. These substrates are produced by slumping commercially available thin glass sheets. In this paper we report on our work of manufacturing these substrates at NASA Goddard Space Flight Center.The NuSTAR mirror assemblies have their heritage in the previously flown balloon payload HEFT (High Energy Focusing Telescope) (Koglin et al. 2005). They use the conical approximation to the traditional Wolter-I optical design. The conical approximation is implemented in two steps: (1) starting with cylindrically-shaped mirror segments whose radii of curvature are within 1 mm of their respective design values; (2) the alignment and integration process bends the cylindrical mirror segments into the required conical shapes and attaches them to the mirror assemblies under the monitoring of real-time metrology. As such the first step of making these mirror assemblies is the manufacture of cylindrically shaped glass substrates.The NuSTAR substrate production is based on a glass slumping technique developed for the International X-ray Observatory (IXO mission, formerly known as the Constellation-X (Zhang et al, 2006) mission. It uses commercially available thin borosilicate glass sheets and slump them on precisely polished and figured fused quartz mandrels. As a result, the finished curved glass is a replica of the mandrel. It takes up the overall shape of the mandrel while preserving the excellent microroughness of the glass sheets.