Summary: An analytical solution of the problem on elastic deformation of a membrane allows analyzing deformation of typical living cells under the influence of magnetic disks attached to the cells. Based on the numerical solution of two-dimensional elliptic boundary value problems, the magnetic polarizabilities of the disks are obtained as the functions of magnetic permeability of the disk substance. It is shown that typical thin disks made of iron, nickel and cobalt in the mode far from saturation are magnetized substantially the same as a disk with infinite magnetic permeability. Though the solved problems are stationary, the results are also usable in the analysis of quasi-stationary processes such as low-frequency variation of external magnetic field.