The analysis of mode conversion caused by discontinuity between K+–Na+ and Ag+–Na+ ion-exchanged waveguides in glass is carried out. The experimentally obtained refractive index profiles of the waveguide regions are considered. Structures consisting of single-mode potassium and 2-, 5-, or 11-mode silver waveguides are studied using the least squares boundary residual method. The power coefficients of light propagation through the interface between the two waveguide regions are evaluated. In the case of structure consisting of a single-mode potassium waveguide and 11-mode silver one, the power transmittance coefficient for the lowest-order transverse electric mode reaches a value of 98.9%.