Layered beams, which use the advantages of various materials in their construction, are widely applied in the construction industry. However, a significant aspect of their design and analysis involves the interlayer connections that may be prone to damage under both static and dynamic conditions. This article examines the influence of interlayer connections on the static response of a simply supported two-layer beam. The analysis is based on mathematical models presented in the literature. Using mathematical analysis methods, a comprehensive static analysis of the Euler–Bernoulli beam was conducted, while assuming that the beam is supported at the bottom edge. When considering the boundary conditions, which are generated by the location of its supports on the two-layer beam, the authors assumed the loading to be in the form of a concentrated force. Solutions regarding the interlayer slip, internal forces, the vertical displacements of the beam, and the stress distributions within the beam were derived. Additionally, the impact of the stiffness of the interlayer connection on the obtained numerical results was investigated. The aim of these studies is to better understand the influence of interlayer connections on the strength and reliability of layered beams, providing valuable design guidelines for engineers working on composite structures.