Microcirculatory vessel response to changes in pressure, known as the myogenic response, is a key component of a tissue's ability to regulate blood flow. Experimental studies have not clearly elucidated the mechanical signal in the vessel wall governing steady-state reduction in vessel diameter upon an increase in intraluminal pressure. In this study, a multiscale computational model is constructed from established models of vessel wall mechanics, vascular smooth muscle (VSM) force generation, and VSM Ca²⁺handling and electrophysiology to compare the plausibility of vessel wall stress or strain as an effective mechanical signal controlling steady-state vascular contraction in the myogenic response. It is shown that, at the scale of a resistance vessel, wall stress, and not stretch (strain), is the likely physiological signal controlling the steady-state myogenic response. The model is then used to test nine candidate VSM stress-controlled channel variants by fitting two separate sets of steady-state myogenic response data. The channel variants include nonselective cation (NSC), supplementary Ca²⁺and Na⁺, L-type Ca²⁺, and large conductance Ca²⁺-activated K⁺channels. The nine variants are tested in turn, and model fits suggest that stress control of Ca²⁺or Na⁺influx through NSC, supplementary Ca²⁺or Na⁺, or L-type Ca²⁺channels is sufficient to produce observed steady-state diameter changes with pressure. However, simulations of steady-state VSM membrane potential, cytosolic Ca²⁺, and Na⁺with pressure show only that Na⁺influx through NSC channel also generates known trends with increasing pressure, indicating that stress-controlled Na⁺influx through NSC is sufficient to generate the myogenic response.