Interactions of sub-nanosecond pulses of kJ-class iodine laser “PALS” with low-density foams and acceleration of Al foils by the pressure of the heated foam matter are investigated here, both experimentally and theoretically. X-ray streak camera is used for evaluation of the speed of energy transfer through the porous foam material. The shock-wave arrival on the rear side of the target is monitored by optical streak camera. Accelerated foil velocities, measured by three-frame optical interferometers, and shadowgraphs, reach up to 107 cm/s. The accelerated foil shape is smooth without any signature of small-scale structures present in the incident laser beam. Conversion efficiencies as high as 14% of the laser energy into the kinetic energy of Al foil are derived. Experimental results compare well with our two-dimensional hydrodynamics simulations and with an approximate analytical model.