A new soft stainless steel sheet has an austenite-stability index Md30 controlled in a range of −120 to −10 and a stacking fault formability index SFI controlled not less than 30, and involves precipitates whose Cu concentration is controlled not more than 1.0%, so as to maintain concentration of dissolved Cu at 1-5%. The stainless steel sheet preferably contains up to 0.06%(C+N), up to 2.0% Si, up to 5% Mn, 15-20% Cr, 5-9% Ni, 1.0-4.0% Cu, up to 0.003% Al, up to 0.005% S, and optionally one or more of up to 0.5% Ti, up to 0.5% Nb, up to 0.5% Zr, up to 0.5% V, up to 3.0% Mo, up to 0.03% B, up to 0.02% REM (rare earth metals) and up to 0.03% Ca. The stainless steel sheet can be plastically deformed to an objective shape without any cracks even at a part heavily-worked part by multi-stage deep drawing or compression deforming. Md30(° C.)=551−462(C+N)−9.2Si−8.1Mn−29(Ni+Cu)−13.7Cr−18.5Mo SFI(mJ/m2)=2.2Ni+6Cu−1.1Cr−13Si−1.2Mn+32.