Pre-stack AVO inversion represents an effective approach for retrieving formation elastic parameters, which has significant implications for fluid identification and reservoir property prediction. However, conventional pre-stack AVO inversion methods based on linearized approximations of the Zoeppritz equation suffer from low accuracy and strong dependence on initial models, and pre-stack stochastic inversion approaches are hindered by poor stability, low computational efficiency, and slow convergence rates. To address these challenges, this study proposes an Adaptive Multi-chain Markov Chain Monte Carlo (AM-MCMC) method for elastic parameter inversion. This method incorporates well-log constrained prior information within a Bayesian framework and constructs a hybrid posterior probability distribution and objective functional based on the exact Zoeppritz equations. By introducing adaptive strategies into the MCMC algorithm, the proposed distributions of the inversion parameters are dynamically adjusted. Multiple Markov chains are employed for stochastic simulation, simultaneously computing statistical characteristic parameters including posterior means, covariances, and confidence intervals of elastic parameters, thereby achieving quantitative characterization of both elastic parameters and their associated uncertainties. Synthetic model tests demonstrate that the stochastic inversion method proposed in this study exhibits superior accuracy, stability, noise immunity, and convergence rate, while also providing reliable uncertainty quantification of the inversion results. Application to field data demonstrates that the near-wellbore seismic inversion results exhibit strong correlation with well-log measurements, validating the method's capability to accurately characterize the elastic properties of gas-bearing tight sandstone reservoirs. This approach shows considerable potential for widespread application in reservoir prediction and reserve evaluation.