  We study the interaction energy of the confining strings in the static
rectangular tetraquark system in SU(3) gluodynamics. Using a two-state
approximation we calculate the energy eigenvalues and corresponding
eigenvectors of string states of different geometry. The interactions are
studied both for the co-aligned and for the counter-aligned parallel strings as
the functions of positions of the tetraquark constituents. We formulate a
simple soap-film model and show that with a good accuracy the string
interaction energy corresponding to the ground state of the tetraquark system
can be described by this soap-film model.
