We study analytically properties of the stress-strain curves family generated by the Boltzmann-Volterra linear viscoelasticity constitutive equation with an arbitrary relaxation modulus under uni-axial loadings at constant strain rates. It is proved (for any decreasing relaxation modulus) that every stress-strain curve is an increasing and convex-up function of strain (without any extremum or inflection points), that stress-strain curves rise up as stress rate increase and that the stress-strain curves family converges to limit curve as stress rate tends to zero or to infinity (i.e. to equilibrium and the instantaneous stress-strain curve). We derived and analyzed the general expression for strain rate sensitivity index of stress-strain curves as the function of strain and strain rate. We found out that the strain rate sensitivity index depends only on the single argument that is the ratio of strain to strain rate. So defined function of one real variable is termed “the strain rate sensitivity function” and it may be regarded as a material function. The explicit integral expression for relaxation modulus via the strain rate sensitivity function is derived. It enables one to restore relaxation modulus assuming a strain rate sensitivity function is given. We proved that the strain rate sensitivity value is confined in the interval from zero to unity (the upper bound of strain rate sensitivity for pseudoplastic media) whatever strain and strain rate are. We found out that the linear theory can reproduce increasing or decreasing or non-monotone dependences of strain rate sensitivity on strain rate (for any fixed strain) and it can provide existence of local maximum. The analysis carried out let us to conclude that the linear viscoelasticity theory (supplied with common relaxation function which are non-exotic from any point of view) is able to produce high values of strain rate sensitivity index close to unity and to provide existence of the strain rate sensitivity index maximum with respect to strain rate. Thus, it is able to simulate qualitatively existence of flexure point on log-log graph of stress dependence on strain rate and its sigmoid shape which is one of the most distinctive features of superplastic deformation regime observed in numerous materials tests.