Abstarct: The problem of seepage analysis has always been one of the most important research topic in the geotechnical as well as hydraulic structural engineering. The ressults of seepage analysis paly a fundamental role through the calculation of discharge flow and also in the designing of the engineering structures such as dams and bridges. Through the recent decades, several approaches (e.g. finite element method, scaled boundary finite element method, finite difference method) have been developed for the seepage analysis of hydraulic structures. However, they have some difficulties arise from the necessity of problem discretization by elements. Aiming to overcome on these shortcomings, meshless methods have been throughly suggested. In the meshless methods there is no need for the problem discretizing by elements or meshes and thus, the problem region is simulated only by the scatered nodes. Deterministic analysis of seepage problems provides an approximate response for discharge flow. In fact, the inherent spatial variability of soil parameters imposes some uncertainties in the solution that causes major errors in results. To incorporate the spatial variability of soils into seepage analyses, the probabilistic approaches must be conducted. In the current thesis, an annovative technique has been proposed for the probabilistic analysis of seepage problems through the foundation of water retaining structures. In this regard, the radial point interpolation method, for mechanical modelling of seepage problem, together with random field theory, for modelling spatial variability, hase been performed within Monte Carlo simulation approach. The random fields of soil permeability (as soil random parameter) were generated by considering the Markov correlation function and also adopting the covariance matrix decomposition algorithm. Finally, to assess the accuracy and efficiency of the proposed probabilistic meshless method, several simulations have been performed with different input parameters and compared well with the results of previous studies. The comparisons confirm the correctness and advantages of the suggested meshless method against other existing solutions. Comparison of the data results from the deterministic and probabilistic simulations show that the calculated water flow rate is always lower than its value in the deterministic analysis. The difference between water flow rates originally depends on the input parameters (i.e. random field correlation length and coefficient of variation of soil permeability). In addition, the results showed that for the highest coefficient of variation (100 %) and the lowest correlation length (1 m), the largest difference in downstream discharge has been achieve. This difference, in this study, is estimated to be about 33 %.