The subject of analytical investigations is a metal seven-layer beam, a plate band with a lengthwise trapezoidal corrugated main core and two crosswise trapezoidal corrugated cores of faces. The hypothesis of deformation of normal to the middle surface of the beam after bending is formulated. Equations of equilibrium are derived based on the theorem of mini- mum total potential energy. The equations are analytically solved. Three point bending and buckling for axially compression of the simply supported beam are theoretically studied. The deflection and the critical axial force are determined for different values of the trapezoidal corrugation pitch of the main core. Moreover, an adequate model of the sandwich beam with steel foam core is formulated. The deflection and the critical axial force are determined for this sandwich beam. The results studied of the seven layer beam and the adequate sandwich beam are compared and presented in tables and figures.