In this paper, a novel matrix-thinning technique, matrix sparse decomposition (MSD) [Liu et al., 1998, 1999], has been implemented to solve the scattering of waves by two-dimensional (2-D) homogeneous dielectric cylinders for the first time. The MSD technique is a further development of the integral equation formulation of the measured equation of invariance (MEI) (IE-MEI) [Rius et al., 1996a; Hirose et al., 1999a]. The MSD describes the local relationship between total currents and scattered fields rather than that between the scattered electric fields and the scattered magnetic fields in the IE-MEI. The MSD directly thins a dense matrix from singular integral equations, such as method of moments (MOM), into two sparse matrices. The IE-MEI method has difficulty in solving thin wire or thin plate structure problems. However, the MSD can do it without a hitch. Numerical examples for the scattering of 2-D homogeneous dielectric circular and rectangular cylinders under both transverse magnetic and transverse electric plane wave incidences show that the MSD is a simple and effective technique to thin the MOM dense matrix.