In summary, we have studied magnetization reversal processes of permalloy nanoparticles of elliptical and rectangular shape by 3D dynamic finite element micromagnetic simulations. The results show the strong influence of the shape and the demagnetizing field on the behavior of the particles. Even without magnetocrystalline anisotropy stable domain configurations with the magnetization perpendicular to the axis of a chain of particles can be obtained. The shape anisotropy and demagnetizing field lead to a spontaneous antiparallel alignment of the magnetization of neighboring particles. If the particles have very small contact faces, a stable configuration with antiparallel magnetization in neighboring particles is found in spite of exchange coupling. This effect can be used in experiments to study magnetoresistive effects in nanoparticles of materials without magnetocrystalline anisotropy.