Accumulation of unfolded/misfolded proteins in neuronal cells perturbs endoplasmic reticulum homeostasis, triggering a stress cascade called unfolded protein response (UPR), markers of which are upregulated in Alzheimer’s disease (AD) brain specimens. We measured the UPR dynamic response in three human neuroblastoma cell lines overexpressing the wild-type and two familial AD (FAD)-associated mutant forms of amyloid precursor protein (APP), the Swedish and Swedish-Indiana mutations, using gene expression analysis. The results reveal a differential response to subsequent environmental stress depending on the genetic background, with cells overexpressing the Swedish variant of APP exhibiting the highest global response. We further developed a dynamic mathematical model of the UPR that describes the activation of the three branches of this stress response in response to unfolded protein accumulation. Model-based analysis of the experimental data suggests that the mutant cell lines experienced a higher protein load and subsequent magnitude of transcriptional activation compared to the cells overexpressing wild-type APP, pointing to higher susceptibility of mutation-carrying cells to stress. The model was then used to understand the effect of therapeutic agents salubrinal, lithium, and valproate on signalling through different UPR branches. This study proposes a novel integrated platform to support the development of therapeutics for AD.