We present a numerical approach for the solution of EM scattering from a dielectric cylinder partially covered with graphene. It is based on a classical Fourier-Bessel expan- sion 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 account. The result is a very simple and very efficient method allow- ing the study of diffraction from such structures.