In this paper we describe the design and characterization of the optical system of LSPE/Strip, a coherent polarimeter array that will observe the microwave sky from the Teide Observatory in Tenerife in two frequency bands centred at 43 and 95 GHz through a dual-reflector crossed-Dragone telescope of 1.5 m aperture. In general, optical systems composed by a telescope-feed array assembly have non-idealities that might limit their ability to perform high-precision measurements. It is thus necessary to understand, characterize and properly control these systematic effects. For this reason, we performed electromagnetic simulations to characterize angular resolution, sidelobes, main beam symmetry, polarization purity and feedhorns orientation. The results presented in this paper will be an essential input for further optical studies and for the LSPE/Strip data analysis. Ultimately, they will be used to assess the impact of optical systematic effects on the scientific results.