The dielectric slabs, dielectric wedges and dielectric rectangular cylinders represent a significant set of structures used in many practical systems. The parameters of interest include field configuration (modes) that can be propagated and scattered by such structures. It is known that power carried by these structures depends upon the constitutive parameters of the medium and the geometry of the structure. The studies carried out so far on the topic of propagation and scattering for these structures is generally due to the slab with very small thickness compared to the wavelength. The approximation solution for the thick dielectric slab is not readily available. The reason is the complexity of the problems. The solutions of these problems result into complicated mathematical formulae which require efficient computational skill which was not available until the advent of fast computers. A solution for the two-dimensional diffraction problem of plane electromagnetic waves by a thick dielectric slab is investigated thoroughly using Mode Matching (MM) technique, which is considered to be straightforward and understandable, in conjunction with the Method of Moment (MoM) considering transverse electric polarizations (TE) parallel to the edge of the considered structure. To start with, the fields in all regions are expanded in terms of mix spectrum of guided and radiated modes. In the free space, a continuous radiation mode expansion is used. The guided modes are finite in number while there are infinite number of radiation modes. The condition for guided modes in the dielectric slab dictates eigenvalue equation. Only those eigenvalues are retained which satisfy valid conditions of the problem. That is, the power is propagated within the slab and and decay exponentially in the free space. Then Mode Matching technique is applied, incorporating the orthogonal properties of the mixed spectrum of the modes in order to separate the guided and radiation components of the field. The discretization of radiation mode spectrum is achieved leading to the numerically stable solution provided a sufficiently large number of points to convert the integral into finite summation. Method of Moment is employed to determine the reflection coefficients for free space radiation modes. Consequently mode amplitudes of all the even guided, odd guided and radiation modes are determined. The scattered far field is evaluated by the saddle point method. A numerical solution of this system is obtained, propagated and scattered powers are evaluated in all regions, which includes the dielectric and free space regions, for various values of incident angles and slab thickness. The same method and sequence is employed for the other dielectric structures like wedge and rectangular cylinder.