The force transmissibility characteristics of a passive vibration isolator in the form of shape memory alloy bar are investigated. The shape memory alloy bar, together with a rigid mass, constitutes a single-degree-of-freedom system. The force isolation ability of the oscillator is evaluated for both isothermal and convective environmental conditions. The transmissibility curve of an isothermal pseudoelastic oscillator displays single and double jumps depending upon the forcing amplitude. The shape memory alloy oscillator with coupled thermomechanical behaviour depends on the cooling rate near resonant frequencies. Increased cooling rate reduces both peak amplitude and the resonant frequency of the transmissibility curve. The force isolation provided by shape memory alloy oscillator is independent of the operating conditions.