Heat and mass transfers inside an adsorbent bed of an adsorption heat pump (AHP) are considered poor; consequently, they can cause low system performance. They should be enhanced so as to increase the coefficient of performance of the cooling machine. The aim of this work is to study an adsorbent bed coated with the zeolite SAPO-34. A simulation model based on governing equations for energy, mass, and momentum transfers is developed using COMSOL Multiphysics software. The system zeolite SAPO-34/water has been considered. Modeling results are validated by experimental database available at the Institute for Advanced Energy Technologies “Nicola Giordano,” Italy. It has been shown that the adsorption heat pump performance is affected by both heat and mass transfer. The enhancement of heat transfer solely is not sufficient to attain high values of specific cooling power. In the case of water vapor/SAPO-34 pair, mass transfer has a significant impact on the duration of the cooling step which should be shortened if one would want to increase the specific cooling power. The sole way to do it is to enhance mass transfer inside porous adsorbent.