<p>In this study, a series of (Ti₃₀Ni₃₅Cu₁₅Zr₂₀)_100-<i>x</i>Y_<i>x</i> (<i>x</i> = 0, 0.5, 1, 2, 5) high-entropy shape memory alloys (HESMAs) were fabricated via vacuum arc melting. The effects of rare earth element yttrium (Y) addition on the microstructure, mechanical properties, superelasticity, and stability of the Ti₃₀Ni₃₅Cu₁₅Zr₂₀ alloy were investigated using scanning electron microscopy (SEM), x-ray diffraction (XRD), energy-dispersive x-ray spectroscopy (EDS), and room temperature cyclic compression tests. The results indicate that the addition of Y within a certain composition range significantly improves the properties of the quaternary Ti₃₀Ni₃₅Cu₁₅Zr₂₀ alloy. Specifically, when the Y content is 0.5 at.% and 1 at.%, the mechanical properties of the high-entropy shape memory alloy are notably enhanced, with the alloy containing 1 at.% Y (Y1) exhibiting the optimal mechanical performance. It possesses a maximum recoverable strain of 8.2%, a superelastic strain of 4.3%, a compressive strength of 1892&#xa0;MPa, and a fracture strain of 16% at room temperature. When the content of Y is 1 at.%, the distribution of precipitated phases in the alloy is relatively uniform, with no obvious local aggregation or sparse regions. The grains are also finer than those of alloys in the same composition group. Among them, the size of the second phase is moderate and its morphology is regular. However, these properties gradually deteriorate when the Y content exceeds 2%. In the cyclic compression tests with a fixed strain of 8%, both the Y0.5 and Y1 alloys achieve a 100% recovery rate after one cycle, and their superelasticity tends to stabilize.</p> Graphical Abstract <p></p>