The results of in-situ neutron diffraction investigation of stress induced martensitic transformation in CuAlZnMn shape memory alloy polycrystal are reported. Time-of-flight diffraction spectra were measured during temporary stopovers along two successive tensile pseudoelastic cycles. The integral intensities, positions and widths of multiple individual austenite and martensite hkl-reflections from the recorded spectra were evaluated by single peak fits. The evaluated peak profile parameters were used to calculate the lattice strains in the austenite phase and volume fractions of the austenite phase evolving during the pseudoelastic cycles. The obtained hkl-lattice plane responses were related to the elastic anisotropy of the cubic austenite phase and to the transformation anisotropy of the β 1 →β' 1 martensitic transformation in CuAlZnMn using a selfconsistent crystallographic model of SMA polycrystals. The mechanism of the load partition among polycrytal grains has been discussed and claimed to be a major obstacle for the stress driven transformability of the polycrystalline Cu-based SMAs It has been found that significant redistribution of stress and large intergranular stresses but no strong transformation induced texture should be expected in Cu based SMA polycrystals transforming pseudoelastically in tension.