A vibroisolation of a payload connected to a vibrating housing by two helical shape memory alloy (SMA) elements is considered. A microstructural theory is used for the simulation of the mechanical behavior of the SMA. The simulations have shown that the resonant frequency and the mitigation of the external vibrations depend on the shape memory alloy state. The maximum reduction of the acceleration amplitude for harmonic excitation is reached when the SMA is in the martensitic pseudoplastic state or in the two-phase state. Variation of temperature allows changing the resonance frequency and thus escaping from resonance. The acceleration of the payload at impact is the smallest when the SMA elements are in the pseudoelastic state.