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.