The Solar-A soft X-Ray telescope is one of several instruments which will be launched aboard the Japanese Solar-A Satellite in 1991, to study the sun during the next period of sunspot activity. Severe launch and on-orbit thermal conditions and the need to provide high resolution over a half minute field of view place unusually stringent requirements upon the mechanical and optical design of this grazing incidence solar x-ray telescope. The instrument must survive an axial acceleration of 18-g, and a lateral acceleration of 7-g over a large vibrational frequency spectrum. A 2.43 arc-sec image quality is specified on-orbit from -2.5 °C to 22.5 °C. In addition, the mount must provide negligible distortion during x-ray testing at 1-g with its optical axis horizontal. This paper describes the process of designing the mirror and mount configuration to successfully meet these demands. As a result of this effort, three unique features were developed which extend the state-of-art in the design of gazing incidence systems. First, by using two hyperbolic surfaces (as suggested by Nariai) instead of the parabola-hyperbola design of a conventional Wolter type I design, a flatter focal plane with better imaging at the edge of the field was obtained. Second, special software was used to link the structural/thermal finite element analysis programs to the optical performance prediction programs. This resulted in a significantly more rapid optimization of both the mechanical design for the critical mounting assembly, and in establishing error budget allocations. Third, the telescope was designed with both hyperbolic optical surfaces in tandem on one substrate, in order to survive launch and guarantee maintenance of alignment between the two surfaces. These design features were successfully demonstrated on the flight model and were fully qualified on the mass model during vibration tests.