Monoliths of microporous aluminophosphates (AlPO₄-17 and AlPO₄-53) were structured by binder-free pulsed current processing. Such monoliths could be important for carbon capture from flue gas. The AlPO₄-17 and AlPO₄-53 monoliths exhibited a tensile strength of 1.0 MPa and a CO₂ adsorption capacity of 2.5 mmol g⁻¹ and 1.6 mmol g⁻¹, respectively at 101 kPa and 0 °C. Analyses of single component CO₂ and N₂ adsorption data indicated that the AlPO₄-53 monoliths had an extraordinarily high CO₂-over-N₂ selectivity from a binary gas mixture of 15 mol% CO₂ and 85 mol% N₂. The estimated CO₂ capture capacity of AlPO₄-17 and AlPO₄-53 monoliths in a typical pressure swing adsorption (PSA) process at 20 °C was higher than that of the commonly used zeolite 13X granules. Under cyclic sorption conditions, AlPO₄-17 and AlPO₄-53 monoliths were regenerated by lowering the pressure of CO₂. Regeneration was done without application of heat, which would regenerate them to their full capacity for CO₂ adsorption.