As critical load-bearing components in aerospace， marine， and construction engineering fields， the buckling stability of plate and shell structures directly determines the safety and reliability of entire systems. However， factors such as material property variability significantly influence the distribution characteristics of critical buckling loads， the traditional deterministic analysis methods are hard to quantify the stochastic influence. The Radial Basis Function （RBF）-enhanced Direct Probability Integral Method （DPIM） is proposed to efficiently determine the probabilistic characteristics of buckling critical loads in plate and shell structures under multiple random variables， which provides theoretical foundations for stochastic buckling uncertainty quantification. By constructing a high-precision explicit surrogate model between critical buckling loads and random variables using RBF， this method effectively reduces the computational cost for implementing the time-consuming buckling finite element analysis in the original direct probability integral method. Comparative analyses with traditional DPIM and Monte Carlo simulation methods in numerical examples demonstrate that the proposed RBF-enhanced DPIM achieves remarkable computational efficiency improvements while maintaining controlled accuracy loss.