## 1 Introduction  
This paper deals with the base plate under a hospital building. It is a reinforced concrete slab that is 500 mm thick, which lies on a layered subsoil. The contact between the base plate and the subsoil only considers the transmission of normal stress, without considering the shear in the foundation joint. The paper is divided into two main parts. The slab is solved by a deterministic and probabilistic approach. We focus on foundation slabs rested on an elastic foundation. From a number of mathematical and material models of the elastic foundation, the model of an elastic half-space (Boussinesq's) was selected. Relationships for stress and strain of an elastic half-space have been described in the literature [1; 2; 3; 4; 5; 6; 7]. From the point of view of the use of computer technology, these are more demanding tasks. The mathematical formulation of the contact problem of the slab and the subsoil, elastic half-space, was described by differential equations. The solution of equations was done by the finite element method (FEM). Because three-dimensional (3D) finite elements are needed to describe an elastic half-space using FEM, we chose the ANSYS system to solve the examples of subsoil slabs. In this solution, where we modeled the elastic half-space as a block of sufficiently large dimensions, the height of a block had an effect in the solution of the problem. This was the depth at which the block, representing the earth body, was supported and was prevented from the vertical displacement. After solving the classical static problem, a case study of the probabilistic calculation followed to assess the reliability of the structure. It is well known that it is not always possible to guarantee the exact properties of the material, geometric arrangement, load, and adherence to the production process. The theory of statistics and probability is always the background of any reliability assessment. Many software programs can evaluate the safety of a structure or its failure, based on probabilistic analysis using the Monte Carlo method, the Latin hypercube sampling (LHS), or the response surface method (RSM). Input parameters are listed as stochastic and are characterized by different types of distribution. Software performs multiple analysis loops to calculate random output parameters as a function of a set of random input variables during probabilistic analysis. Uncertainties in the input variables (load, material properties, and geometrical dimensions) are reflected in the RSM based on the approximation of Monte Carlo simulations [8; 9; 10; 11; 12]. The base plate was, thus, assessed on the serviceability limit state (SLS) and the control function was deflection. Such calculations can contribute to the safety of structures. The aim of the article is to point out the need to use probabilistic methods in the field of interaction of foundation structures with subsoil. Subsoil, which is a material whose properties are highly variable, is suitable for demonstrating the use of probability theories. The article should be an example of the need and use of probabilistic theories in the contact field of building structures with a flexible subsoil.