Astrocytes participate in brain functions through Ca(2+) signals, including Ca(2+) waves and Ca(2+) oscillations. Currently the mechanisms of Ca(2+) signals in astrocytes are not fully clear. Here, we present a computational model to specify the relative contributions of different Ca(2+) flows between the extracellular space, the cytoplasm and the endoplasmic reticulum of astrocytes to the generation of spontaneous Ca(2+) oscillations (CASs) and cortical spreading depression (CSD)-triggered Ca(2+) waves (CSDCWs) in a one-dimensional astrocyte network. This model shows that CASs depend primarily on Ca(2+) released from internal stores of astrocytes, and CSDCWs depend mainly on voltage-gated Ca(2+) influx. It predicts that voltage-gated Ca(2+) influx is able to generate Ca(2+) waves during the process of CSD even after depleting internal Ca(2+) stores. Furthermore, the model investigates the interactions between CASs and CSDCWs and shows that the pass of CSDCWs suppresses CASs, whereas CASs do not prevent the generation of CSDCWs. This work quantitatively analyzes the generation of astrocytic Ca(2+) signals and indicates different mechanisms underlying CSDCWs and non-CSDCWs. Research on the different types of Ca(2+) signals might help to understand the ways by which astrocytes participate in information processing in brain functions.