A low background double-wall piston-cylinder-type pressure cell is developed at the Paul Scherrer Institute. The cell is made from BERLYCO-25 (beryllium copper) and MP35N nonmagnetic alloys with the design and dimensions which are specifically adapted to muon-spin rotation/relaxation (muSR) measurements. The mechanical design and performance of the pressure cell are evaluated using finite-element analysis (FEA). By including the measured stress-strain characteristics of the material into the finite-element model, the cell dimensions are optimized with the aim to reach the highest possible pressure while maintaining the sample space large (6 mm in diameter and 12 mm high). The presented unconventional design of the double-wall piston-cylinder pressure cell with a harder outer MP35N sleeve and asofter inner CuBe cylinder enables pressures of up to 2.6 GPa to be reached at ambient temperatures, corresponding to 2.2 GPa at low temperatures without any irreversible damage to the pressure cell. The nature of the muon stopping distribution, mainly in the sample and in the CuBe cylinder, results in a low-background muSR signal.