A method for constructing three‐dimensional solenoidal magnetization distributions, with invariant magnitude ofm, in arbitrarily shaped objects is presented. The formalism harks back to the theory developed by van den Berg for two‐dimensionalmdistributions. The space within a general object &OHgr; is partitioned intoisubspaces &OHgr;i, described by a family of surfaces to which the magnetization is tangent. A characteristic equation which defines the course ofmat each of the surfaces is derived. A boundary condition formarises naturally, or can be chosen to determinemat the surface. Within the above framework an infinite number of solutions are generated that, in general, exhibit singularities. Special attention, also from the topological point of view, is paid to themdistributions having point defects only.