Abstract:Background. The purpose of this work is to study numerically TE-polarized waves in a layer filled with various dielectric materials. Material and methods. In order to obtain a numerical solution to the problem, the parameter shooting method is used. Results. Complex and propagating leaky waves, complex and propagating surface waves were numericially found. Conclusions. The proposed numerical method is an effective way to find an approximate solution to the problem of propagation of electromagnetic waves.