Abstarct: In conventional analyzes of soil failure, the soil strengh parameters are assumed to be constant and deterministic even at large strains. This is while during failure, soil strength shows maximum and residual amounts and its strength decreases progressively with the increase of plastic strain. maximum and residual amounts, and its strength decreases prematurely by increasing the plastic strain. In addition to changing soil strengh parameters in the progressive mechanism, the non-uniform nature of the soil also causes locative variations of these parameters. Therefore, geotechnical systems should be investigated with the partial uncertainty of the soil non-deterministically and using the concepts of statistics and probabilities. Progressive failure is deterministic or non-deterministic only by using numerical techniques such as the finite element method that are able to simulate the development of deviatoric plastic strain. Although the finite element method is specifically used in the analysis of stability problems, it faces problems that are primarily related to meshing. In this research, the method of point interpolation with radial functions in combination with random field is used to model changes in the mechanism of soil strength properties and analysis of soil instability. In order to consider the progressive failure of the soil, the elastoplastic solution method with developed Moore-Coulomb behavior model is used. To perform probabilities, the random field of cohesion and friction angle baxsed on their mean values and standard deviation In order to investigate the application of the point interpolation method with random radial functions, an soil slope and a foundation with specified geometries were analyzed deterministic and non-deterministic and the safety factor was checked. In the following, by performing probabilistic analysis and generating random fields, the probabilistic functions of the safety factors are determined, and considering that all non-deterministic parameters are assumed to be normal using the log input, the probability density function of the safety factor is also of the same type of distribution. compliance and fits on the histogram. By determining the probability density function, the cumulative distribution function can also be determined. With this result, we can conclude that probably the slope and foundation with progressive failure and the changes of strength mechanisms will be less than the criterion of failure will be 68 and 14%. This number actually represents the probability of failure of the slope or foundation under investigation. In the following, by determining probabilistic functions from similar statistics, deviation, reliability index, probability of failure and coefficient of variation have been determined. The analysis by means of progressive failure modeling, it is concluded that real soil failure and continuous displacements come to the environment simultaneously with the formation of the progressive mechanism of soil deterioration and reaching the sliding path to the earth's surface. The safety factor values are transferred from the safe state to the critical region by changing the values of the parameters from the maximum value to the residual value. Therefore, the type of failure is progressive. lixnk Also, it is observed that the changes of safety factor obtained from the method of interpolation of points with radial functions are placed in limited intervals compared to other methods. Therefore, according to the obtained results, it is possible to use the point interpolation method with random radial functions as a suitable numerical method with the ability to model the probabilities of the main soil changes in various geotechnical problems.