Laser shock peening (LSP) is a non-contact surface treatment method that has been experimentally found to help increase fracture toughness, induce near-surface compressive residual stress and increase hardness in ceramic materials. Numerous experiments, with associated costs and challenges, are needed to identify the application-specific LSP parameters. Physics-based computational models provide a less expensive and more flexible alternative to performing the requisite experiments, yet the trade-off between computational cost and accuracy of different models needs to be considered. In this work, LSP treatment finite element simulations are executed using a calibrated Drucker-Prager (DP) plasticity model combined with a Mie-Grüneisen equation of state as well as Johnson-Cook rate dependence and a damage initiation criterion. Unlike existing Johnson-Holmquist (JH) methods, the calibrated DP constitutive model does not require damage model parameters to be continually updated with deformation, resulting in lower computational time. Near-surface compressive residual stress, predicted by the model, is compared to measurements reported in recent experimental studies. At the lowest pulse energy tested (1 J) an approximate 5% difference exists between the simulated RS and that measured by Raman spectroscopy in the experiments. This difference appears to increase with greater pulse energies. A parametric comparison of computational time for differences in laser pulse energy, constitutive models, and materials is also performed. Results reveal that the demonstrated model at the lowest pulse energy on alumina is up to 37.5% faster, and when applied to silicon carbide, is up to 15.7% faster in comparison to existing JH methods.