A magnetization model is presented that is used to cover trilayers containing two magnetic layers that are exchange coupled via an intermediate nonmagnetic layer and that have different crystalline anisotropies. The interfaces are coupled to the bulk by a twisted magnetization configuration which is evaluated using the Ritz method. By minimizing the total energy, experimental magnetization curves of strongly coupled Co/Ru sandwiches can be reproduced with a good precision and with the same set of parameters in two perpendicular field directions. These physical parameters can be determined with a good reliability and are in agreement with the literature except for the bulk anisotropy of the Co layer first deposited, which is twice as large as the known bulk value. This originates in the magnetoelastic contributions due to lattice misfit and interface roughness. It is shown that the interlayer exchange coupling forces the magnetization of both layers to be along the same axis in the low‐field range notwithstanding the opposite sign of the anisotropy constants in most stacks. It is also demonstrated that the differences in the orientations of the moments in one Co layer are modest and depend on the various parameters. In particular, the bulk exchange constant is a decisive parameter that makes the calculated curves close to the experimental ones. ©1996 American Institute of Physics.