A new X-ray method of generalized pole figures (GPF) was developed to determine the distribution of microstrains in alpha-Zr grains of Zr-based alloy tubes for the needs of nuclear industry. The method uses the Warren approach by the treatment of X-ray line profiles, acquired separately for all grain orientations by successive positions of the sample in the course of texture measurements. For the first time, obtained values of the lattice strain epsilon along ctystallographic axes <0001> were presented as the distribution depending on the orientation (psi,phi) of these axes in the stereographic projection of the studied tube sample, as well as distributions of grain volume fractions v(epsilon).