A study was conducted to understand and predict initial failure locations, their paths, and failure stresses of specimens with a circular hole and loaded by a bolt. The polymethyl methacrylate (PMMA) material was used to make six different types of specimens which had three different widths with a circular hole of its diameter 8 mm and different hole locations along the specimen length. All the specimens were loaded using a bolt inserted into the hole with three different bolts of nominal diameters of 8 mm, 6 mm, and 5 mm, respectively. To predict the results obtained from physical tests, the recently proposed universal failure criterion was used in the study using the finite element analyses. The maximum normal stresses and its gradients were considered to predict the failure locations, their directions, and failure stresses. The predicted failure characteristics were acceptable when compared to the experimental results.