Stacks of superconducting tapes can trap much higher magnetic fields than conventional magnets. This makes them very promising for motors and generators. However, ripple magnetic fields in these machines present a cross-field component that demagnetizes the stacks. At present, there is no quantitative agreement between measurements and modeling, mainly due to the need of a 3D model that takes the real micron-thick superconducting layer into account. This article presents 3D modeling and measurements of cross-field demagnetization in stacks of up to 5 tapes and initial magnetization modeling of stacks of up to 15 tapes. 3D modeling of the cross-field demagnetization shows that the critical current density, \(J_c\), in the \(c\)-axis does not play a role in cross-field demagnetization. When taking the measured anisotropic magnetic field dependence of \(J_c\) into account, calculations agree with measurements with less than 4 \% deviation. Then, our 3D numerical methods can realistically predict cross-field demagnetization. Due to the force-free configuration of part of the current density, \(J\), in the stack, better agreement with experiments will require measurement of the \(J_c\) anisotropy for the whole solid angle range, including \(J\) parallel to the magnetic field.