Shaped charge is widely used in petroleum drilling, yet the inherent parametric uncertainty of oil shale introduces significant uncertainties that affect perforation outcomes. The complex coupling of oil shale constitutive parameters under extreme strains poses challenges for uncertainty quantification. A coupled algorithm integrating an improved material point method (MPM) and polynomial chaos expansion (PCE) is presented, and polynomial chaos expansion (PCE) is used to systematically analyze the uncertainty and sensitivity of shaped charge jet penetration depth. Mechanical parameters from oil shale samples at Checun Coal Mine well No. 1 were tested to define key parameter ranges and establish a reliable uncertainty space. A benchmark simulation of a single isolated shaped charge jet validated the algorithm, and Sobol’ global sensitivity analysis identified internal friction angle, density, and Poisson’s ratio as strongly sensitive parameters, while tensile strength, Young’s modulus, and cohesion showed weak sensitivity, supporting surrogate model dimensionality reduction. Composite detonation models of three and five charges further revealed the effects of multi-projectile blast wave coupling on jet dynamics, providing new theoretical insights into cluster effects under high-energy, high-pressure, and extreme-strain conditions. Sensitivity and uncertainty analyses based on surrogate models emphasized the critical influence of internal friction angle alongside Poisson’s ratio and density. A reliable numerical framework is established for multi-physics coupled simulations of geomechanical responses under complex multi-source explosive loading.