Some considerations on structural and thermal designs on 4 MJ pulsed superconducting magnet are described. By using a model which simulates one of the double pancake coils of the magnet, the turn-to-turn propagation of electromagnetic force is analyzed. It is clarified that the force would hardly be transmitted when the Young's modulus perpendicular to the flat surface of the cable is small, that is, about a few hundred kg/mm**2 and that a Young's modulus of more than 1,000 kg/mm**2 will be required in order that the force may be transmitted sufficiently. In the thermal design of the magnet, a horizontal velocity of the helium bubbles which exist in the 3 degree-tapering cooling channels is calculated.