The problem of the flexural vibrations of two semi-infinite elastic plates connected along a section of the boundary (the joint) that is short compared with the wavelength of the incident wave, is considered. The problem is reduced to solving integral equations on the section. The use of Green's formula leads to an integral equation with a smooth kernel, the solution of which is a function with singularities of order - 32 at the ends of the section. Regularization of this integral equation is carried out. The asymptotic form of the far field over the dimensionless length of the joint is found.