This article discusses the effects of the stiffness and confinement ratios of shape memory alloy (SMA) wire jackets on the behavior of confined concrete. SMA wire jackets are an effective confining material to improve concrete behavior; for example, by increasing peak strength and failure strain. The stiffness and confinement ratios of fiber-reinforced polymer jackets have been extensively discussed and their effects are well known. However, assessment of the stiffness and confinement ratios of SMA wire jackets has not previously been conducted. In this study, we investigate the effects of the stiffness and confinement ratios of steel jackets, and then compare the results with those of SMA wire jackets. In general, the stiffness ratios of SMA wire jackets are relatively smaller than those of steel jackets, and most of them have lower stiffness ratios because the Young’s moduli of the SMAs are relatively small. The active confining pressure of the SMA wires does not improve the lower stiffness-ratio effect since the amount of active confining pressure is not sufficiently large.