Local effects that occur in the vicinity of junctions between different cores in sandwich panels subjected to the in-plane axial force and bending moment are considered. These local effects manifest themselves in a rise of locally induced bending normal stresses in the sandwich faces and shear and normal stresses in the cores in the near vicinity of the core junctions. Intensity of the local effects is measured experimentally for a representative sandwich beam subjected to both types of loadings. The numerical simulations are performed using Finite Element Analysis, and they reveal significant rates of stress concentrations in the faces and cores adjacent to the core junctions. The intensity of the local effects is dependable on the geometry and elastic properties of the sandwich faces and a degree of dissimilarity of elastic properties of the adjoined cores.