Initiation of martensitic unelasticity effects in TiNi, Cu-Al-Ni and Cu-Al-Mn by variation of the hydrostatic pressure has been studied. The experiments have been carried out in the high-pressure chamber involving an electric heater and a system for strain and stress measurements. It has been found that the pressure decreases the characteristic temperatures of the martensitic transformation for all studied alloys. Because of this an isothermal increase of the pressure on the stage of the direct transformation produces a temperature delay of the strain variation at further cooling and, vice versa, an isothermal decrease of the pressure causes the continuation of the transformation and a strain growth. Similarly, the pressure variation can initiate strain recovery or its temperature delay at subsequent heating. It has been found that the shifts of the characteristic temperatures caused by the pressure are bigger than one can expect considering only the volume change at the transformation. Other factors, which may be responsible for the observed temperature shift are discussed.