UK molecular R-matrix calculations have been carried out for electron scattering from anthracene and pyrene. These molecules belong to the family of polycyclic hydrocarbons (PAHs) and are found in a nebula known as the Red Rectangle. Static exchange (SE), static exchange plus polarization (SEP), and close coupling (CC) approximations are used for scattering calculations. Different elastic and inelastic cross sections are computed in the present work in the energy range of 0.1-15 eV. Dissociative electron attachment cross sections are also calculated for both the molecules. Various shape, Feshbach/core-excited, and mixed resonances are detected for these molecules below 10 eV. All of the resonances detected in the present study are in agreement with the existing experimental and theoretical results. Due to the complexity of the present targets, electron collision cross sections are essentially unknown and hence most of the results are presented for the first time.