In this paper, the dynamic response of clamped rectangular sandwich tubes with metal foam core under transverse blast loading is analytically and numerically studied. First, based on the theory of the solid beam subjected to transverse blast loading, a semi-empirical analytical solution for the dynamic response of rectangular hollow metal tube is given subjected to transverse blast loading considering local denting effect and combined axial force and bending moment. Then, based on the analytical solution for the dynamic response of the metal tube, a semi-empirical analytical solution for the dynamic response of clamped rectangular sandwich tubes with metal foam core under transverse blast loading is obtained. The numerical calculation for the dynamic response of clamped rectangular sandwich tubes is carried out. The numerical results locate between the upper and lower bounds of the analytical solution. Next, using the least square method, an analytical method to predict the maximum deflection of sandwich tubes is given under no experimental or numerical data conditions based on the existing data. The present analytical method can be used to predict the dynamic response of clamped rectangular sandwich tubes with metal foam core under transverse blast loading. Also, the comparison of energy absorption between rectangular sandwich tube with metal foam core and rectangular hollow tube for the same mass is conducted. It is shown that the sandwich tube is better than the hollow tube in terms of energy absorption in large deflection.