The article proposes models of nonlinear estimation of the bearing capacity of piles on weathered claystone and sandstone. These soils are often used as the foundation for deep foundations for critical structures such as bridges, transport structures, dams. Often, laboratory tests of such soils give underestimated values of the characteristics. As a result, the bearing capacity of the designed pile foundations is much more than necessary. The main goal of this study is to develop equations that allow us to evaluate the bearing capacity of the pile foundation in these soils by a non-destructive method. The authors propose semi-empirical equations based on analytical solutions and empirical data, obtained from plate-bearing tests. These equations can be used for an estimation of the bearing capacity of piles of various diameters without conducting expensive field tests. Assessment of the obtained equations reliability showed that the determination coefficient is 0.90 for claystone, and 0.96 for sandstone. This allows us to characterize the obtained approximating functions as theoretical models of good quality. Proposed equations was compared with other methods and static load test results.