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We have investigated the superconducting properties of monofilament MgB2 tapes and wires with a stainless steel (SUS316) sheath. MgB2 powder was put into a SUS316 tube with a 6.5 mm diameter; the tube was cold-rolled into a wire with a 1.4 mm-1.0 mm diameter using groove-rolling and cassette roller dies and then cold-rolled into tapes. The stainless steel sheath is effective to increase the density of the MgB2 core. The transport critical current density depends on the wire diameter and tape thickness. The JC values increase with increasing the total cross-sectional area reduction of tapes. However, the JC value of the tape with a thickness of less than 0.3 mm deteriorated because of cracks introduced by rolling. Post-annealing increased the JC properties of these tapes. The low annealing temperature of ∼600°C was effective to increase the JC values for MgB2/(stainless steel) tapes. This temperature was much lower than the optimum annealing temperature of MgB2 tapes with other sheath materials, such as MgB2/Fe tapes. The post-annealing improved the linkage of grains and enhanced the JC values.