Saliva is an essential part of activities such as speaking, masticating and swallowing. Enzymes in salivary fluid protect teeth and gums from infectious diseases, and also initiate the digestion process. Intracellular calcium (Ca2+) plays a critical role in saliva secretion and regulation. Experimental measurements of Ca2+ and inositol trisphosphate (IP3) concentrations in HSY cells, a human salivary duct cell line, show that when the cells are stimulated with adenosine triphosphate (ATP) or carbachol (CCh), they exhibit coupled oscillations with Ca2+ spike peaks preceding IP3 spike peaks. Based on these data, we construct a mathematical model of coupled Ca2+ and IP3 oscillations in HSY cells and perform model simulations of three different experimental settings to forecast Ca2+ responses. The model predicts that when Ca2+ influx from the extracellular space is removed, oscillations gradually slow down until they stop. The model simulation of applying a pulse of IP3 predicts that photolysis of caged IP3 causes a transient increase in the frequency of the Ca2+ oscillations. Lastly, when Ca2+-dependent activation of PLC is inhibited, we see an increase in the oscillation frequency and a decrease in the amplitude. These model predictions are confirmed by experimental data. We conclude that, although concentrations of Ca2+ and IP3 oscillate, Ca2+ oscillations in HSY cells are the result of modulation of the IP3 receptor by intracellular Ca2+, and that the period is modulated by the accompanying IP3 oscillations.