Elastic foundation supports represent a configuration in which a beam, typically made of a solid material, rests on a deformable or elastic foundation. This type of system is encountered in various engineering applications, such as civil engineering, structural design, and geotechnical engineering, where structures like bridges, buildings, and platforms are connected to the ground. Elastic foundation supports are statically indeterminate systems for which external reactions cannot be determined by equilibrium equations as in the case of statically determinate beams. Therefore, it is necessary to find boundary conditions at certain characteristic points. Unlike determinate and indeterminate statically determined systems where external reactions are represented as concentrated forces or moments, the external reaction of the foundation is a continuous loading. This assumption is based on Winkler's theory that the foundation reaction is proportional to the foundation deflection. The paper discusses some of the basic methods for calculating internal forces and deformations for examples of beam systems supported on an elastic foundation and compares them with the results obtained from the software analysis of the SpBeam program, which operates on the principle of the stiffness method, or finite element method. By comparing the results obtained from analytical calculations and software results, a difference of approximately 10% is observed.