In this paper, the experimentally observed significant increase in yield stress for strain rates beyond 10⁴ s⁻¹ (viscous regime) is explicitly considered in laser shock processing (LSP) simulations. First, a detailed review of the most common high-strain-rate deformation models is presented, highlighting the expected strain rates in materials subject to LSP for a wide range of treatment conditions. Second, the abrupt yield stress increase presented beyond 10⁴ s⁻¹ is explicitly considered in the material model of a titanium alloy subject to LSP. A combined numerical–analytical approach is used to predict the time evolution of the plastic strain. Finally, extended areas are irradiated covering a squared area of 25 × 25 mm² for numerical–experimental validation. The in-depth experimental residual stress profiles are obtained by means of the hole drilling method. Near-surface-temperature gradients are explicitly considered in simulations. In summary, the conventionally accepted strain rate range in LSP (10⁶–10⁷ s⁻¹) is challenged in this paper. Results show that the conventional high-strain-rate hardening models widely used in LSP simulations (i.e., Johnson Cook model) clearly overestimate the induced compressive residual stresses. Additionally, pressure decay, whose importance is usually neglected, has been found to play a significant role in the total plastic strain achieved by LSP treatments.