New methods of foundation bed reliability calculations by the criterion of the shift when the base is under the influence of horizontal (shifting) forces are made. Initial statistical information is limited. Random variables in the calculation model are described by distribution functions of possibility (from the theory of possibility), distribution functions received from Chebyshev's inequality; combination of functions. The size of controlled parameters measurements (statistical information) for reliability calculations is small in practice and sometimes it doesn't allow to carry out their statistical analysis for the use of probabilistic and statistical methods of reliability calculations of the foundation beds. The considerable decrease in reliability of the foundation bed causes soil moistening as, for example, it is now in the Far East the Russian Federation. When there is a lack of time for collecting of information for an assessment of buildings and constructions safety, the developed techniques can be used. In this work such situation is illustrated by the example.