A pseudo-strain energy function (pseudo-SEF) describing the biomechanical properties of large conduit arteries under the influence of vascular smooth muscle (VSM) tone is proposed. In contrast to previous models that include the effects of the smooth muscle contraction through generation of an active stress, in this study we consider the vascular muscle as a structural element whose contribution to load-bearing is modulated by the contraction. This novel pseudo-SEF not only models arterial mechanics at maximal VSM contraction, but also the myogenic contraction of the VSM in response to local increases in stretch. The proposed pseudo-SEF was verified using experimentally obtained pressure-radius (p-r) curves and zero stress state configurations from rat carotid arteries displaying distinct differences in VSM tone: arteries from normotensive rats displaying minimal VSM tone and arteries from hypertensive rats exhibiting significant VSM tone. The p-r curves were measured in three different VSM states: fully relaxed, maximally contracted, and normal VSM tone. The model fitted the experimental data very well (r² > 0.99) in both the normo- and hypertensive groups for all three states of VSM activation. The pseudo-SEF was used to illustrate the localized reduction of circumferential stress in the arterial wall due to normal VSM tone suggesting that the proposed pseudo-SEF can be of general utility for describing stress distribution not only under passive VSM conditions, as most SEFs proposed so far, but also under physiological and pathological conditions with varying levels of VSM tone.