The accumulation of unfolded proteins in the endoplasmic reticulum (ER) activates a mechanism whose primary functions are to sense any perturbation in the protein-folding capacity of the cell, and correct the situation to restore homeostasis. This cellular mechanism is called the unfolded protein response (UPR). We propose a biologically plausible computational model for the UPR under ER stress in mammalian cells. The model accounts for the signaling pathways of PERK, ATF6, and IRE1 and has the advantage of simulating the dynamical (timecourse) changes in the relative concentrations of proteins without any a priori steady-state assumption. Several types of ER stress can be assumed as input, including long-term (eventually periodic) stress. Moreover, the model allows for outcomes ranging from cell survival to cell apoptosis.