We present a numerical approach for the solution of EM scattering from a dielectric cylinder partially covered with graphene. It is based on a clas- sical Fourier-Bessel expansion of the fields inside and outside the cylinder to which we apply the ad-hoc boundary conditions in the presence of graphene. Due to the singular nature of the electric field at the ends of the graphene sheet, we introduce auxiliary boundary conditions to better take this reality into ac- count. The result is a very simple and very efficient method allowing the study of diffraction from such structures. Our ultimate goal is to apply this approach to radiative heat transfer between graphene coated cylinders and planes.