A hybrid finite difference time domain-boundary integral equation approach is used to model frequency selective surfaces of finite extent. Using the finite difference time domain technique, a system matrix is constructed for a box enclosing all relevant features within a unit cell. The open character of the finite frequency selective surface is modeled by coupling a boundary integral equation formulation to the system matrix found with the finite difference time domain approach. A number of relevant examples are studied, and a comparison is made between our new technique and the more classical finite difference time domain technique or the hybrid finite element-boundary integral equation method. ¿ 2000 American Geophysical Union