The problem of ambiguity in the definition of lattice rotation, used in plastic deformation models, is examined in this work. The geometry of tensile and compression deformation is considered. Two approaches to lattice rotation are considered: the classical definition (called also ‘mathematical analysis’) and the definition based on orientation preservation of specified directions/planes in the sample coordinates system. Similar study was already done by the present authors for the geometry of rolling deformation. It was shown that application of two rotation definitions enables to explain the appearance of two types of f.c.c. rolling textures: brass type and copper type textures. In the case of axisymmetric deformation the application of both definitions of lattice rotation leads to similar textures, but with different spread of their principal components.