The pulsatile deformations of the large arteries can be viewed as small time-varying deformations superposed on large deformations. This motivates the study of the incremental deformations of the vascular tissue. Unfortunately, because of the variety of possible choices of definitions of stresses and strains, the choice of the characterizing incremental moduli is not unique, which has led to much ambiguity and confusion in the literature. This communication systematically presents some of the options available for characterization of orthotropic incremental deformations of the vascular tissue, and provides explicit formulas for interconversions of incremental elastic moduli for uniaxial tests on strips of incompressible tissue. Relative merits of various choices are discussed.