This study focuses on the development of a Fokker-Planck-Kolmogorov equation-based theory of probabilistic elastoplasticity and its application to stochastic geomechanics boundary value problems. Part I contains a brief review of the most common uncertainty quantification methods relative to the problem under investigation as well as a review of the uncertainty characteristics of geomaterials, which is the medium of interest herein. In Part II, the theory of probabilistic elastoplasticity, first introduced by Jeremić et al.(2007), is modified after presenting the limitations associated with the original development. In addition, a new inelastic theory is proposed that is based on minimum entropy principles and deviates from classical plasticity theory formulations. A meshless numerical solution procedure for the solution of the underlying nonlinear Fokker-Planck-Kolmogorov equation is also developed based on radial basis …