The magnetization value and electric resistivity of the single-crystalline sample of Ni50Fe19Co4Ga27 shape memory alloy were measured. The elastic modulus was determined by the Dynamic Mechanical Analysis (DMA). The characteristic temperatures of martensitic transformation (MT) of the alloy were estimated from the temperature dependences of magnetization, electric resistivity and elastic modulus. A significant disparity between MT temperatures resulting from DMA and those estimated from magnetic and resistivity measurements was discovered. It was argued that the discrepancy is caused by the non-uniform mechanical stressing of twinned single crystal by the DMA analyzer. Moreover, the DMA measurements revealed a significant decrease of the elastic modulus of twinned martensite under the applied magnetic field of 1.5 kOe. To explain this effect, the temperature-dependent Young’s modulus of twinned crystal lattice was computed. The computations showed that the experimentally observed field-induced change of the elastic modulus is caused by the stress-assisted detwinning of the crystal lattice by the applied magnetic field.