As an unusual mechanical response, the ferroelastic phenomenon in two-dimensional materials has been reported both experimentally and theoretically in recent years. Here, we present the theoretical findings of ferroelastic switching in monolayer PdS2. We demonstrate four types of PdS2 allotropes, showing excellent ferroelasticity with low ferroelastic barriers and strong switching signals. The ferroelastic transitions in monolayer PdS2 include the lattice rotation in penta-α PdS2, the transformation between penta-α PdS2 and penta-β PdS2, the transformation between penta-α PdS2 and penta-γ PdS2, the transformation between penta-β PdS2 and penta-γ PdS2, the transformation between penta-α PdS2 and δ PdS2, and the lattice rotation in δ PdS2. The ferroelastic transitions between these four allotropes have revealed the flexible ferroelasticity in monolayer PdS2. Specifically, the flexible switching in PdS2 allotropes may efficiently control the anisotropic transport of electrons. Thus, the presence of these outstanding mechanical properties endows PdS2 with great potential for applications in next-generation shape memory devices.