Stress granules (SGs) are non-membranous cytoplasmic aggregates of mRNAs and related proteins, assembled in response to environmental stresses such as heat shock, hypoxia, endoplasmic reticulum (ER) stress, chemicals (e.g. arsenite), and viral infections. SGs are hypothesized as a loci of mRNA triage and/or maintenance of proper translation capacity ratio to the pool of mRNAs. In brain ischemia, hippocampal CA3 neurons, which are resilient to ischemia, assemble SGs. In contrast, CA1 neurons, which are vulnerable to ischemia, do not assemble SGs. These results suggest a critical role SG plays in regards to cell fate decisions. Thus SG assembly along with its dynamics should determine the cell fate. However, the process that exactly determines the SG assembly dynamics is largely unknown. In this paper, analyses of experimental data and computer simulations were used to approach this problem. SGs were assembled as a result of applying arsenite to HeLa cells. The number of SGs increased after a short latent period, reached a maximum, then decreased during the application of arsenite. At the same time, the size of SGs grew larger and became localized at the perinuclear region. A minimal mathematical model was constructed, and stochastic simulations were run to test the modeling. Since SGs are discrete entities as there are only several tens of them in a cell, commonly used deterministic simulations could not be employed. The stochastic simulations replicated observed dynamics of SG assembly. In addition, these stochastic simulations predicted a gamma distribution relative to the size of SGs. This same distribution was also found in our experimental data suggesting the existence of multiple fusion steps in the SG assembly. Furthermore, we found that the initial steps in the SG assembly process and microtubules were critical to the dynamics. Thus our experiments and stochastic simulations presented a possible mechanism regulating SG assembly.