  In this paper I developed a classical model of elementary particle that is
associated with a membrane of finite size, surrounded by non-linear
electromagnetic field. The form of local interaction which lead to bounded
states of finite masses, charges and spins was constructed. To do this I added
Kaluza-Klein Lagrangian on the surface, which is associated with extended
particle, to quadratic in field potentials term (a la tachyon mass). This
ensures that Lagrangian remains an even function of the field, but spontaneous
symmetry breaking leads to nontrivial soliton-like solutions. I assumed that
the particle has axial symmetry and that the surface has only one degree of
freedom, i.e. is a disk with the radius determined from the equations of
motion. The solution of system of two non-linear partial differential equations
for the field potentials was obtained numerically by different methods. Several
solutions with increasing orders of leading field multipoles and disk radius
were obtained, and masses, electric charges and spins were calculated. In the
framework of this model the ratio of a charge square to a double spin, i.e. the
fine structure constant, which do not depend on parameters of the model, was
calculated.
