A numerical analysis based on the finite element method is developed to simulate the mechanical response of a typical sixteen-ounce plastic drink cup subjected to a lateral compressive load. The aim of the analysis is to simulate a test in which the cup is supported horizontally in a fixture on a testing machine platen, and a loading nose attached to the actuator is displaced downward into the cup. The numerical model is developed using the software packages MSC.Patran, ABAQUS/CAE, and ABAQUS/Standard. The high impact polystyrene material of the cup is modeled as linear elastic, considering isotropic and orthotropic material behavior. The structural model of the cup is a truncated conical shell including a ring at the open end of the cup and circumferential stiffening ribs. The analysis is based on small strain, large rotation shell kinematics, and the loading apparatus of the test is simulated with a rigid, circular cylinder contacting the cup. Coupons cut from the wall of a cup are subjected to tension to determine the ranges of the meridional and circumferential moduli of elasticity. Rings cut from the open end of the cup were tested in diametrical tension to aid in validating the finite element modeling. Reasonable correlation of the simulation to available cup compression test data is achieved. Parametric studies are conducted for several meridional thickness distributions of the cup wall, and for a range of orthotropic material properties. / Master of Science