To gain insight into the mechanisms that underlie Angiotensin II (Ang II) induced [Ca]_cyt oscillations in medullary pericytes, we expanded a prior model of ion fluxes. Ang II stimulation was simulated by doubling maximal IP₃ production and imposing a 90% blockade of K⁺ channels. We investigated two configurations, one in which ryanodyne receptors (RyR) and inositol trisphophate receptors (IP₃R) occupy a common store and a second in which they reside on separate stores. Our results suggest that the Ca²⁺ release from stores and import from the extracellular space are key determinants of oscillations because both raise Ca²⁺ concentration in subplasmalemmal spaces near RyR. When the Ca²⁺ induced Ca²⁺ release (CICR) threshold of RyR is exceeded, the ensuing Ca²⁺ release is limited by Ca²⁺ re-uptake into stores and export across the plasmalemma. If SERCA pumps do not remain saturated and SR Ca²⁺ stores are replenished, that phase is followed by a resumption of leak from internal stores that leads either to [Ca]_cyt elevation below the CICR threshold (no oscillations) or elevation above it (oscillations). Our model predicts that oscillations are more prone to occur when IP₃R and RyR stores are separate because, in that case, Ca²⁺ released by RyR during CICR can enhance filling of adjacent IP₃ stores to favor a high subsequent leak that generates further CICR events. Moreover, the existence or absence of oscillations depends on the set points of several parameters so that biological variation might well explain the presence or absence of oscillations in individual pericytes.