A thin, penetrable, and cylindrical reflector is illuminated by the incident field of a complex source point. The scattered field inside the reflector is not considered and its effect is modelled through a thin layer generalised boundary condition (GBC). The authors formulate the structure as an electromagnetic boundary value problem and two resultant coupled singular integral equation system of equations are solved by using regularisation techniques. The GBC provides us to simulate the thin layer better than the resistive model which is applicable only for very thin sheets. Hence, the more reliable data can be obtained for high-contrast and low-loss dielectric material. The scattering and absorption characteristics of the front-fed and offset reflectors are obtained depending on system parameters. Also, the effects of the edge loading are examined for both E- and H-polarisations. The convergence and the accuracy of the formulation are verified in reasonable computational running time.