A simplified model of magnetomechanical coupling for hard magnetoactive elastomers (h-MAEs) is developed, notable for its computational speed and good agreement with experiments. The model is based on the forces acting on magnetic dipoles in a magnetic field. It utilizes the finite element method, with each element represented as a magnetic dipole. The fabrication process and the simulation of magnetic-field-induced deformation of a soft gripper made of h-MAE are conducted. The mechanical properties are measured using tensile testing and the magnetic characteristics are evaluated through magnetic hysteresis loops. The deformation of the gripper is analyzed with digital image correlation and compared to the simulation results. The model provides efficient and fast computation with reliable results, facilitating the design of soft robots with various functionalities.