This study investigated the mechanisms underlying the propagation of cytoplasmic calcium waves and the genesis of systolic Ca(2+) alternans in cardiac myocytes lacking transverse tubules (t-tubules). These correspond to atrial cells of either small mammals or large mammals that have lost their t-tubules due to disease-induced structural remodeling (e.g., atrial fibrillation). A mathematical model was developed for a cluster of ryanodine receptors distributed on the cross section of a cell that was divided into 13 elements with a spatial resolution of 2 μm. Due to the absence of t-tubules, L-type Ca(2+) channels were only located in the peripheral elements close to the cell-membrane surface and produced Ca(2+) signals that propagated toward central elements by triggering successive Ca(2+)-induced Ca(2+) release (CICR) via Ca(2+) diffusion between adjacent elements. Under control conditions, the Ca(2+) signals did not fully propagate to the central region of the cell. However, with modulation of several factors responsible for Ca(2+) handling, such as the L-type Ca(2+) channels (Ca(2+) influx), SERCA pumps (sarcoplasmic reticulum (SR) Ca(2+) uptake), and ryanodine receptors (SR Ca(2+) release), Ca(2+) wave propagation to the center of the cell could occur. These simulation results are consistent with previous experimental data from atrial cells of small mammals. The model further reveals that spatially functional heterogeneity in Ca(2+) diffusion within the cell produced a steep relationship between the SR Ca(2+) content and the cytoplasmic Ca(2+) concentration. This played an important role in the genesis of Ca(2+) alternans that were more obvious in central than in peripheral elements. Possible association between the occurrence of Ca(2+) alternans and the model parameters of Ca(2+) handling was comprehensively explored in a wide range of one- and two-parameter spaces. In addition, the model revealed a spontaneous second Ca(2+) release in response to a single voltage stimulus pulse with SR Ca(2+) overloading and augmented Ca(2+) influx. This study provides what to our knowledge are new insights into the genesis of Ca(2+) alternans and spontaneous second Ca(2+) release in cardiac myocytes that lack t-tubules.