Tensile stability of healthy medial arterial tissue and its constituents, subject to initial geometrical and/or material imperfections, is investigated based on the long wavelength approximation. The study employs existing constitutive models for elastin, collagen, and vascular smooth muscle which comprise the medial layer of large elastic (conducting) arteries. A composite constitutive model is presented based on the concept of the musculoelastic fascicle (MEF) which is taken to be the essential building block of medial arterial tissue. Nonlinear equations governing axial stretch and areal stretch imperfection growth quantities are obtained and solved numerically. Exact, closed-form results are presented for both initial and terminal rates of imperfection growth with nominal load. The results reveal that geometrical imperfections, in the form of area nonuniformities, and material imperfections, in the form of constitutive parameter nonuniformities, either decrease or increase only slightly with increasing nominal load; a result which is to be expected for healthy tissue. By way of contrast, an examination of a simple model for elastin with a degrading stiffness gives rise to unbounded imperfection growth rates at finite values of nominal load. The latter result indicates how initial geometrical and material imperfections in diseased tissues might behave, a topic of future study by the authors.